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Journal articles on the topic 'Graph algorithmics'
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1
Meyer, Ulrich, and Manuel Penschuck. "Large-scale graph generation: Recent results of the SPP 1736 – Part II." it - Information Technology 62, no. 3-4 (May 27, 2020): 135–44. http://dx.doi.org/10.1515/itit-2019-0041.
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AbstractThe selection of input data is a crucial step in virtually every empirical study. Experimental campaigns in algorithm engineering, experimental algorithmics, network analysis, and many other fields often require suited network data. In this context, synthetic graphs play an important role, as data sets of observed networks are typically scarce, biased, not sufficiently understood, and may pose logistic and legal challenges. Just like processing huge graphs becomes challenging in the big data setting, new algorithmic approaches are necessary to generate such massive instances efficiently. Here, we update our previous survey [35] on results for large-scale graph generation obtained within the DFG priority programme SPP 1736 (Algorithms for Big Data); to this end, we broaden the scope and include recently published results.
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Mihelič, Jurij, and Uroš Čibej. "An experimental evaluation of refinement techniques for the subgraph isomorphism backtracking algorithms." Open Computer Science 11, no. 1 (December 17, 2020): 33–42. http://dx.doi.org/10.1515/comp-2020-0149.
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AbstractIn this paper, we study a well-known computationally hard problem, called the subgraph isomorphism problem where the goal is for a given pattern and target graphs to determine whether the pattern is a subgraph of the target graph. Numerous algorithms for solving the problem exist in the literature and most of them are based on the backtracking approach. Since straightforward backtracking is usually slow, many algorithmic refinement techniques are used in practical algorithms. The main goal of this paper is to study such refinement techniques and to determine their ability to speed up backtracking algorithms. To do this we use a methodology of experimental algorithmics. We perform an experimental evaluation of the techniques and their combinations and, hence, demonstrate their usefulness in practice.
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Reddy, K. Krishna Mohan, P. Renjith, and N. Sadagopan. "Listing all spanning trees in Halin graphs — sequential and Parallel view." Discrete Mathematics, Algorithms and Applications 10, no. 01 (February 2018): 1850005. http://dx.doi.org/10.1142/s1793830918500052.
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For a connected labeled graph [Formula: see text], a spanning tree [Formula: see text] is a connected and acyclic subgraph that spans all vertices of [Formula: see text]. In this paper, we consider a classical combinatorial problem which is to list all spanning trees of [Formula: see text]. A Halin graph is a graph obtained from a tree with no degree two vertices and by joining all leaves with a cycle. We present a sequential and parallel algorithm to enumerate all spanning trees in Halin graphs. Our approach enumerates without repetitions and we make use of [Formula: see text] processors for parallel algorithmics, where [Formula: see text] and [Formula: see text] are the depth, the number of leaves, respectively, of the Halin graph. We also prove that the number of spanning trees in Halin graphs is [Formula: see text].
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Bentert, Matthias, Leon Kellerhals, and Rolf Niedermeier. "Fair Short Paths in Vertex-Colored Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 10 (June 26, 2023): 12346–54. http://dx.doi.org/10.1609/aaai.v37i10.26455.
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The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a group (color), we provide a framework to model multiple natural fairness aspects. We seek to find short paths in which the number of occurrences of each color is within some given lower and upper bounds. Among other results, we prove the introduced problems to be computationally intractable (NP-hard and parameterized hard with respect to the number of colors) even in very restricted settings (such as each color should appear with exactly the same frequency), while also presenting an encouraging algorithmic result ("fixed-parameter tractability") related to the length of the sought solution path for the general problem.
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Casteigts, Arnaud, Anne-Sophie Himmel, Hendrik Molter, and Philipp Zschoche. "Finding Temporal Paths Under Waiting Time Constraints." Algorithmica 83, no. 9 (June 4, 2021): 2754–802. http://dx.doi.org/10.1007/s00453-021-00831-w.
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AbstractComputing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes over time, gained more and more attention. A path is time-respecting, or temporal, if it uses edges with non-decreasing time stamps. We investigate a basic constraint for temporal paths, where the time spent at each vertex must not exceed a given duration $$\varDelta $$ Δ , referred to as $$\varDelta $$ Δ -restless temporal paths. This constraint arises naturally in the modeling of real-world processes like packet routing in communication networks and infection transmission routes of diseases where recovery confers lasting resistance. While finding temporal paths without waiting time restrictions is known to be doable in polynomial time, we show that the “restless variant” of this problem becomes computationally hard even in very restrictive settings. For example, it is W[1]-hard when parameterized by the distance to disjoint path of the underlying graph, which implies W[1]-hardness for many other parameters like feedback vertex number and pathwidth. A natural question is thus whether the problem becomes tractable in some natural settings. We explore several natural parameterizations, presenting FPT algorithms for three kinds of parameters: (1) output-related parameters (here, the maximum length of the path), (2) classical parameters applied to the underlying graph (e.g., feedback edge number), and (3) a new parameter called timed feedback vertex number, which captures finer-grained temporal features of the input temporal graph, and which may be of interest beyond this work.
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Ji, Shengwei, Chenyang Bu, Lei Li, and Xindong Wu. "Local Graph Edge Partitioning." ACM Transactions on Intelligent Systems and Technology 12, no. 5 (October 31, 2021): 1–25. http://dx.doi.org/10.1145/3466685.
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Graph edge partitioning, which is essential for the efficiency of distributed graph computation systems, divides a graph into several balanced partitions within a given size to minimize the number of vertices to be cut. Existing graph partitioning models can be classified into two categories: offline and streaming graph partitioning models. The former requires global graph information during the partitioning, which is expensive in terms of time and memory for large-scale graphs. The latter creates partitions based solely on the received graph information. However, the streaming model may result in a lower partitioning quality compared with the offline model. Therefore, this study introduces a Local Graph Edge Partitioning model, which considers only the local information (i.e., a portion of a graph instead of the entire graph) during the partitioning. Considering only the local graph information is meaningful because acquiring complete information for large-scale graphs is expensive. Based on the Local Graph Edge Partitioning model, two local graph edge partitioning algorithms—Two-stage Local Partitioning and Adaptive Local Partitioning—are given. Experimental results obtained on 14 real-world graphs demonstrate that the proposed algorithms outperform rival algorithms in most tested cases. Furthermore, the proposed algorithms are proven to significantly improve the efficiency of the real graph computation system GraphX.
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Cappelletti, Luca, Tommaso Fontana, Elena Casiraghi, Vida Ravanmehr, Tiffany J. Callahan, Carlos Cano, Marcin P. Joachimiak, et al. "GRAPE for fast and scalable graph processing and random-walk-based embedding." Nature Computational Science 3, no. 6 (June 26, 2023): 552–68. http://dx.doi.org/10.1038/s43588-023-00465-8.
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AbstractGraph representation learning methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are beyond the capabilities of current methods and software implementations. We present GRAPE (Graph Representation Learning, Prediction and Evaluation), a software resource for graph processing and embedding that is able to scale with big graphs by using specialized and smart data structures, algorithms, and a fast parallel implementation of random-walk-based methods. Compared with state-of-the-art software resources, GRAPE shows an improvement of orders of magnitude in empirical space and time complexity, as well as competitive edge- and node-label prediction performance. GRAPE comprises approximately 1.7 million well-documented lines of Python and Rust code and provides 69 node-embedding methods, 25 inference models, a collection of efficient graph-processing utilities, and over 80,000 graphs from the literature and other sources. Standardized interfaces allow a seamless integration of third-party libraries, while ready-to-use and modular pipelines permit an easy-to-use evaluation of graph-representation-learning methods, therefore also positioning GRAPE as a software resource that performs a fair comparison between methods and libraries for graph processing and embedding.
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Ergenç Bostanoğlu, Belgin, and Nourhan Abuzayed. "Dynamic frequent subgraph mining algorithms over evolving graphs: a survey." PeerJ Computer Science 10 (October 8, 2024): e2361. http://dx.doi.org/10.7717/peerj-cs.2361.
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Frequent subgraph mining (FSM) is an essential and challenging graph mining task used in several applications of the modern data science. Some of the FSM algorithms have the objective of finding all frequent subgraphs whereas some of the algorithms focus on discovering frequent subgraphs approximately. On the other hand, modern applications employ evolving graphs where the increments are small graphs or stream of nodes and edges. In such cases, FSM task becomes more challenging due to growing data size and complexity of the base algorithms. Recently we see frequent subgraph mining algorithms designed for dynamic graph data. However, there is no comparative review of the dynamic subgraph mining algorithms focusing on the discovery of frequent subgraphs over evolving graph data. This article focuses on the characteristics of dynamic frequent subgraph mining algorithms over evolving graphs. We first introduce and compare dynamic frequent subgraph mining algorithms; trying to highlight their attributes as increment type, graph type, graph representation, internal data structure, algorithmic approach, programming approach, base algorithm and output type. Secondly, we introduce and compare the approximate frequent subgraph mining algorithms for dynamic graphs with additional attributes as their sampling strategy, data in the sample, statistical guarantees on the sample and their main objective. Finally, we highlight research opportunities in this specific domain from our perspective. Overall, we aim to introduce the research area of frequent subgraph mining over evolving graphs with the hope that this can serve as a reference and inspiration for the researchers of the field.
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Nikolopoulos, Stavros D., and Leonidas Palios. "Parallel Algorithms for Recognizing P5-free and ${\bar P}_5$-free Weakly Chordal Graphs." Parallel Processing Letters 14, no. 01 (March 2004): 119–29. http://dx.doi.org/10.1142/s0129626404001763.
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We prove algorithmic characterizations of weakly chordal graphs, which lead to efficient parallel algorithms for recognizing P5-free and [Formula: see text]-free weakly chordal graphs. For an input graph on n vertices and m edges, our algorithms run in O( log 2n) time and require O(m2/ log n) processors on the EREW PRAM model of computation. The proposed recognition algorithms efficiently detect P5 s and [Formula: see text] in weakly chordal graphs in O( log n) time with O(m2/ log n) processors on the EREW PRAM. Additionally, we show how the algorithms can be augmented to provide a certificate for the existence of a P5 (or a [Formula: see text]) in case the input graph is not P5-free (respectively, [Formula: see text]-free) weakly chordal.
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KHOUSSAINOV, BAKHADYR, JIAMOU LIU, and MIA MINNES. "Unary automatic graphs: an algorithmic perspective." Mathematical Structures in Computer Science 19, no. 1 (February 2009): 133–52. http://dx.doi.org/10.1017/s0960129508007342.
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This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced using such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by finite automata over the unary alphabet). We investigate algorithmic properties of such unfolded graphs given their finite presentations. In particular, we ask whether a given node belongs to an infinite component, whether two given nodes in the graph are reachable from one another and whether the graph is connected. We give polynomial-time algorithms for each of these questions. For a fixed input graph, the algorithm for the first question is in constant time and the second question is decided using an automaton that recognises the reachability relation in a uniform way. Hence, we improve on previous work, in which non-elementary or non-uniform algorithms were found.
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Manaster, Alfred B., Jeffrey B. Remmel, and James H. Schmerl. "Planarity and minimal path algorithms." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 1 (February 1986): 131–42. http://dx.doi.org/10.1017/s1446788700026550.
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AbstractIn 1981 two notions of effective presentation of countable connected graphs were formulated by J. C. E. Dekker—namely, edge recognition algorithm graphs and minimal path algorithm graphs. In this paper we show that every planar graph has a minimal path algorithm presentation but that some graphs have no minimal path algorithm presentations. We introduce the notion of a shortest distance algorithm graph, show that it lies strictly between the two notions of Dekker, and show that every graph has a shortest distance algorithm presentation. Finally, in contrast to Dekker's result about minimal path algorithm graphs, we produce a shortest distance algorithm graph which has no spanning tree which is an edge recognition algorithm graph.
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FANKHAUSER, STEFAN, KASPAR RIESEN, HORST BUNKE, and PETER DICKINSON. "SUBOPTIMAL GRAPH ISOMORPHISM USING BIPARTITE MATCHING." International Journal of Pattern Recognition and Artificial Intelligence 26, no. 06 (September 2012): 1250013. http://dx.doi.org/10.1142/s0218001412500139.
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Graphs provide us with a flexible and powerful way to represent objects in various areas of computer science. One of the main drawbacks is, however, that many standard algorithms on graphs have a high computational complexity. The present paper considers the problem of graph isomorphism, i.e. checking two graphs for identity. A novel approach for the efficient computation of graph isomorphism is presented. The proposed algorithm is based on bipartite graph matching by means of an assignment algorithm. The algorithmic framework is suboptimal in the sense of possibly rejecting pairs of graphs without making a decision. As an advantage, however, it offers polynomial runtime. In experiments on diverse graph data sets we demonstrate substantial speedups of our proposed method over several standard procedures for graph isomorphism. Furthermore, although the computational framework for isomorphism is suboptimal, we show that the proposed algorithm rejects only very few pairs of graphs and otherwise returns correct results.
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Möhring, Rolf H. "Algorithmic graph theory and perfect graphs." Order 3, no. 2 (June 1986): 207–8. http://dx.doi.org/10.1007/bf00390110.
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Güvenoglu, Büsra, and Belgin Ergenç Bostanoglu. "A qualitative survey on frequent subgraph mining." Open Computer Science 8, no. 1 (December 1, 2018): 194–209. http://dx.doi.org/10.1515/comp-2018-0018.
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AbstractData mining is a popular research area that has been studied by many researchers and focuses on finding unforeseen and important information in large databases. One of the popular data structures used to represent large heterogeneous data in the field of data mining is graphs. So, graph mining is one of the most popular subdivisions of data mining. Subgraphs that are more frequently encountered than the user-defined threshold in a database are called frequent subgraphs. Frequent subgraphs in a database can give important information about this database. Using this information, data can be classified, clustered and indexed. The purpose of this survey is to examine frequent subgraph mining algorithms (i) in terms of frequent subgraph discovery process phases such as candidate generation and frequency calculation, (ii) categorize the algorithms according to their general attributes such as input type, dynamicity of graphs, result type, algorithmic approach they are based on, algorithmic design and graph representation as well as (iii) to discuss the performance of algorithms in comparison to each other and the challenges faced by the algorithms recently.
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GAVRIL, FANICA. "ALGORITHMS ON SUBGRAPH OVERLAP GRAPHS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (March 19, 2014): 1450018. http://dx.doi.org/10.1142/s1793830914500189.
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Consider a graph D and a family FI of connected edge subgraphs of D. Let GI(V, F) be the intersection graph of FI and G the overlap graph of FI. We describe polynomial time algorithms for subgraph overlap graphs G when their intersection graphs GI have specific hereditary properties. The algorithms are to find maximum induced complete bipartite subgraphs, maximum weight holes of a given parity, minimum dominating holes, antiholes of a given parity and some others. In addition, we define the family of subgraph filament graphs based on D, FI and GI, and prove it to be the same as the family of subgraph overlap graphs.
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ERWIG, MARTIN. "Inductive graphs and functional graph algorithms." Journal of Functional Programming 11, no. 5 (August 29, 2001): 467–92. http://dx.doi.org/10.1017/s0956796801004075.
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We propose a new style of writing graph algorithms in functional languages which is based on an alternative view of graphs as inductively defined data types. We show how this graph model can be implemented efficiently, and then we demonstrate how graph algorithms can be succinctly given by recursive function definitions based on the inductive graph view. We also regard this as a contribution to the teaching of algorithms and data structures in functional languages since we can use the functional-style graph algorithms instead of the imperative algorithms that are dominant today.
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Cusack, Charles A., Aaron Green, Airat Bekmetjev, and Mark Powers. "Graph pebbling algorithms and Lemke graphs." Discrete Applied Mathematics 262 (June 2019): 72–82. http://dx.doi.org/10.1016/j.dam.2019.02.028.
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Doc, Nguyen Van, Nguyen Minh Giam, Nguyen Thi Hoai Nam, Ngo Tu Thanh, and Nguyen Thi Huong Giang. "Applying Algorithmic Thinking to Teaching Graphs of Functions For Students Through Geogebra." Journal of Education For Sustainable Innovation 1, no. 2 (December 3, 2023): 85–94. http://dx.doi.org/10.56916/jesi.v1i2.554.
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Algorithmic thinking is a term that is of interest to many educators and teachers. Algorithmic thinking plays an important role not only in problem solving but also in solving real world problems. The article presents some concepts of algorithmic thinking; propose the process of applying algorithmic thinking to teaching function graphs for students through GeoGebra online, helping students to draw all functions in the fastest way. GeoGebra is integrated with algorithms used to graph any function online that students cannot do. GeoGebra is used effectively, interactively and actively supported by many students, students and teachers of Mathematics in the process of graphing functions and graphs in an intuitive and detailed way, thereby developing develop students' thinking.
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Molnár, Bálint, and András Benczúr. "The Application of Directed Hyper-Graphs for Analysis of Models of Information Systems." Mathematics 10, no. 5 (February 27, 2022): 759. http://dx.doi.org/10.3390/math10050759.
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Hyper-graphs offer the opportunity to formulate logical statements about their components, for example, using Horn clauses. Several models of Information Systems can be represented using hyper-graphs as the workflows, i.e., the business processes. During the modeling of Information Systems, many constraints should be maintained during the development process. The models of Information Systems are complex objects, for this reason, the analysis of algorithms and graph structures that can support the consistency and integrity of models is an essential issue. A set of interdependencies between models and components of architecture can be formulated by functional dependencies and can be investigated via algorithmic methods. Information Systems can be perceived as overarching documents that includes data collections; documents to be processed; and representations of business processes, activities, and services. Whe selecting and working out an appropriate method encoding of artifacts in Information Systems, the complex structure can be represented using hyper-graphs. This representation enables the application of various model-checking, verification, and validation tools that are based on formal approaches. This paper describes the proposed representations in different situations using hyper-graphs, moreover, the formal, algorithmic-based model-checking methods that are coupled with the representations. The model-checking methods are realized by algorithms that are grounded in graph-theoretical approaches and tailored to the specificity of hyper-graphs. Finally, the possible applications in a real-life enterprise environment are outlined.
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Chen, Yuzhong, Zhenyu Liu, Yulin Liu, and Chen Dong. "Distributed Attack Modeling Approach Based on Process Mining and Graph Segmentation." Entropy 22, no. 9 (September 14, 2020): 1026. http://dx.doi.org/10.3390/e22091026.
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Attack graph modeling aims to generate attack models by investigating attack behaviors recorded in intrusion alerts raised in network security devices. Attack models can help network security administrators discover an attack strategy that intruders use to compromise the network and implement a timely response to security threats. However, the state-of-the-art algorithms for attack graph modeling are unable to obtain a high-level or global-oriented view of the attack strategy. To address the aforementioned issue, considering the similarity between attack behavior and workflow, we employ a heuristic process mining algorithm to generate the initial attack graph. Although the initial attack graphs generated by the heuristic process mining algorithm are complete, they are extremely complex for manual analysis. To improve their readability, we propose a graph segmentation algorithm to split a complex attack graph into multiple subgraphs while preserving the original structure. Furthermore, to handle massive volume alert data, we propose a distributed attack graph generation algorithm based on Hadoop MapReduce and a distributed attack graph segmentation algorithm based on Spark GraphX. Additionally, we conduct comprehensive experiments to validate the performance of the proposed algorithms. The experimental results demonstrate that the proposed algorithms achieve considerable improvement over comparative algorithms in terms of accuracy and efficiency.
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Dhulipala, Laxman, Guy E. Blelloch, and Julian Shun. "Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable." ACM Transactions on Parallel Computing 8, no. 1 (April 2021): 1–70. http://dx.doi.org/10.1145/3434393.
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There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the interfaces, optimizations, and graph processing techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph Based Benchmark Suite (GBBS).
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Formanowicz, Piotr, and Krzysztof Tanaś. "The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks." International Journal of Applied Mathematics and Computer Science 22, no. 3 (October 1, 2012): 765–78. http://dx.doi.org/10.2478/v10006-012-0057-y.
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Abstract It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan–Raspaud conjecture.
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Cicerone, Serafino, and Gabriele Di Stefano. "Getting new algorithmic results by extending distance-hereditary graphs via split composition." PeerJ Computer Science 7 (July 7, 2021): e627. http://dx.doi.org/10.7717/peerj-cs.627.
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In this paper, we consider the graph class denoted as Gen(∗;P3,C3,C5). It contains all graphs that can be generated by the split composition operation using path P3, cycle C3, and any cycle C5 as components. This graph class extends the well-known class of distance-hereditary graphs, which corresponds, according to the adopted generative notation, to Gen(∗;P3,C3). We also use the concept of stretch number for providing a relationship between Gen(∗;P3,C3) and the hierarchy formed by the graph classes DH(k), with k ≥1, where DH(1) also coincides with the class of distance-hereditary graphs. For the addressed graph class, we prove there exist efficient algorithms for several basic combinatorial problems, like recognition, stretch number, stability number, clique number, domination number, chromatic number, and graph isomorphism. We also prove that graphs in the new class have bounded clique-width.
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SKULRATTANAKULCHAI, SAN, and HAROLD N. GABOW. "COLORING ALGORITHMS ON SUBCUBIC GRAPHS." International Journal of Foundations of Computer Science 15, no. 01 (February 2004): 21–40. http://dx.doi.org/10.1142/s0129054104002285.
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We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM algorithm for the same problem. It uses O(n/ log n) processors and runs in O( log n) time with high probability, where n is the number of vertices of the graph. The third algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The fourth algorithm generalizes this to get the first linear-time algorithm to 5-list-total-color subcubic graphs. Our sequential algorithms are based on a method of ordering the vertices and edges by traversing a spanning tree of a graph in a bottom-up fashion. Our parallel algorithm is based on a simple decomposition principle for subcubic graphs.
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DEHKORDI, HOOMAN REISI, and PETER EADES. "EVERY OUTER-1-PLANE GRAPH HAS A RIGHT ANGLE CROSSING DRAWING." International Journal of Computational Geometry & Applications 22, no. 06 (December 2012): 543–57. http://dx.doi.org/10.1142/s021819591250015x.
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There is strong empirical evidence that human perception of a graph drawing is negatively correlated with the number of edge crossings. However, recent experiments show that one can reduce the negative effect by ensuring that the edges that cross do so at large angles. These experiments have motivated a number of mathematical and algorithmic studies of “right angle crossing (RAC)” drawings of graphs, where the edges cross each other perpendicularly. In this paper we give an algorithm for constructing RAC drawings of “outer-1-plane” graphs, that is, topological graphs in which each vertex appears on the outer face, and each edge crosses at most one other edge. The drawing algorithm preserves the embedding of the input graph. This is one of the few algorithms available to construct RAC drawings.
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Shahzad, Muhammad, Muhammad Ahsan Asim, Roslan Hasni, and Ali Ahmad. "Computing Edge Irregularity Strength of Star and Banana Trees Using Algorithmic Approach." Ars Combinatoria 159, no. 1 (June 30, 2024): 11–20. http://dx.doi.org/10.61091/ars159-02.
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After the Chartrand definition of graph labeling, since 1988 many graph families have been labeled through mathematical techniques. A basic approach in those labelings was to find a pattern among the labels and then prove them using sequences and series formulae. In 2018, Asim applied computer-based algorithms to overcome this limitation and label such families where mathematical solutions were either not available or the solution was not optimum. Asim et al. in 2018 introduced the algorithmic solution in the area of edge irregular labeling for computing a better upper-bound of the complete graph \(es(K_n)\) and a tight upper-bound for the complete \(m\)-ary tree \({es(T}_{m,h})\) using computer-based experiments. Later on, more problems like complete bipartite and circulant graphs were solved using the same technique. Algorithmic solutions opened a new horizon for researchers to customize these algorithms for other types of labeling and for more complex graphs. In this article, to compute edge irregular \(k\)-labeling of star \(S_{m,n}\) and banana tree \({BT}_{m,n}\), new algorithms are designed, and results are obtained by executing them on computers. To validate the results of computer-based experiments with mathematical theorems, inductive reasoning is adopted. Tabulated results are analyzed using the law of double inequality and it is concluded that both families of trees observe the property of edge irregularity strength and are tight for \(\left\lceil \frac{|V|}{2} \right\rceil\)-labeling.
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Dib, Fadi K., and Peter Rodgers. "Graph drawing using Jaya." PLOS ONE 18, no. 6 (June 27, 2023): e0287744. http://dx.doi.org/10.1371/journal.pone.0287744.
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Graph drawing, involving the automatic layout of graphs, is vital for clear data visualization and interpretation but poses challenges due to the optimization of a multi-metric objective function, an area where current search-based methods seek improvement. In this paper, we investigate the performance of Jaya algorithm for automatic graph layout with straight lines. Jaya algorithm has not been previously used in the field of graph drawing. Unlike most population-based methods, Jaya algorithm is a parameter-less algorithm in that it requires no algorithm-specific control parameters and only population size and number of iterations need to be specified, which makes it easy for researchers to apply in the field. To improve Jaya algorithm’s performance, we applied Latin Hypercube Sampling to initialize the population of individuals so that they widely cover the search space. We developed a visualization tool that simplifies the integration of search methods, allowing for easy performance testing of algorithms on graphs with weighted aesthetic metrics. We benchmarked the Jaya algorithm and its enhanced version against Hill Climbing and Simulated Annealing, commonly used graph-drawing search algorithms which have a limited number of parameters, to demonstrate Jaya algorithm’s effectiveness in the field. We conducted experiments on synthetic datasets with varying numbers of nodes and edges using the Erdős–Rényi model and real-world graph datasets and evaluated the quality of the generated layouts, and the performance of the methods based on number of function evaluations. We also conducted a scalability experiment on Jaya algorithm to evaluate its ability to handle large-scale graphs. Our results showed that Jaya algorithm significantly outperforms Hill Climbing and Simulated Annealing in terms of the quality of the generated graph layouts and the speed at which the layouts were produced. Using improved population sampling generated better layouts compared to the original Jaya algorithm using the same number of function evaluations. Moreover, Jaya algorithm was able to draw layouts for graphs with 500 nodes in a reasonable time.
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Wang, Yishu, Ye Yuan, Yuliang Ma, and Guoren Wang. "Time-Dependent Graphs: Definitions, Applications, and Algorithms." Data Science and Engineering 4, no. 4 (September 25, 2019): 352–66. http://dx.doi.org/10.1007/s41019-019-00105-0.
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Abstract A time-dependent graph is, informally speaking, a graph structure dynamically changes with time. In such graphs, the weights associated with edges dynamically change over time, that is, the edges in such graphs are activated by sequences of time-dependent elements. Many real-life scenarios can be better modeled by time-dependent graphs, such as bioinformatics networks, transportation networks, and social networks. In particular, the time-dependent graph is a very broad concept, which is reflected in the related research with many names, including temporal graphs, evolving graphs, time-varying graphs, historical graphs, and so on. Though static graphs have been extensively studied, for their time-dependent generalizations, we are still far from a complete and mature theory of models and algorithms. In this paper, we discuss the definition and topological structure of time-dependent graphs, as well as models for their relationship to dynamic systems. In addition, we review some classic problems on time-dependent graphs, e.g., route planning, social analysis, and subgraph problem (including matching and mining). We also introduce existing time-dependent systems and summarize their advantages and limitations. We try to keep the descriptions consistent as much as possible and we hope the survey can help practitioners to understand existing time-dependent techniques.
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Khalid Hamad Alnafisah, Khalid Hamad Alnafisah. "An Algorithmic Solution for the “Hair Ball” Problem in Data Visualization." Journal of engineering sciences and information technology 2, no. 4 (December 30, 2018): 86–66. http://dx.doi.org/10.26389/ajsrp.k220918.
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The investigation and analysis of large and complex graphs is an important aspect of data visualization research, yet there is a need for entirely new, scalable approaches and methodologies for graph visualization. This can ultimately provide more insight into the structure and function of this complex graph (Hair Ball). To explain more, we need to find a methodology to develop a solution to present a “Tidy” graph with the minimal crossover between edges in the “Hair Balls.” In spite of the expanding significance of investigating and extensively analyzing and understanding very large graphs of data, the traditional way of visualizing graphs has difficulties scaling up, and typically ends up depicting these large graphs as “Hair Balls”. This traditional approach does indeed have a deeply intuitive foundation: nodes are depicted with a shape such as a circle, triangle or square, which are then connected by lines or curves that represent the edges. In any case, although there are many different ways to apply this basic underlying idea, it needs to be revisited in light of current and emerging needs for understanding increasingly complex crossover between edges in the graphs. The complex “Hair Ball,” which appears as an indecipherable graph, came from the crossover between edges. From our preliminary research, we found the major disadvantage in the Hair Balls graph was that it confused observers. Users may think there are some extra nodes; but in reality, there are not. Because there are many crossovers between edges in the Hair Balls, the impression also may affect observers’ understanding of the whole structure of the graph. Major problem-no effective reception of information from a “Hair Balls” graph-meaningless to observers.
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Bakonyi, Mihály, and Erik M. Varness. "Algorithmic aspects of bipartite graphs." International Journal of Mathematics and Mathematical Sciences 18, no. 2 (1995): 299–304. http://dx.doi.org/10.1155/s0161171295000378.
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We generalize previous work done by Donald J. Rose and Robert E. Tarjan [2], who developed efficient algorithms for use on directed graphs. This paper considers an edge elimination process on bipartite graphs, presenting several theorems which lead to an algorithm for computing the minimal fill-in of a given ordered graph.
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Serratosa, Francesc. "A Methodology to Generate Attributed Graphs with a Bounded Graph Edit Distance for Graph-Matching Testing." International Journal of Pattern Recognition and Artificial Intelligence 32, no. 11 (July 24, 2018): 1850038. http://dx.doi.org/10.1142/s0218001418500386.
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This paper presents a methodology for generating pairs of attributed graphs with a lower and upper- bounded graph edit distance (GED). It is independent of the type of attributes on nodes and edges. The algorithm is composed of three steps: randomly generating a graph, generating another graph as a sub-graph of the first, and adding structural and semantic noise to both. These graphs, together with their bounded distances, can be used to manufacture synthetic databases of large graphs. The exact GED between large graphs cannot be obtained for runtime reasons since it has to be computed through an optimal algorithm with an exponential computational cost. Through this database, we can test the behavior of the known or new sub-optimal error-tolerant graph-matching algorithms against a lower and an upper bound GED on large graphs, even though we do not have the true distance. It is not clear how the error induced by the use of sub-optimal algorithms grows with problem size. Thus, with this methodology, we can generate graph databases and analyze if the current assumption that we can extrapolate algorithms’ behavior from matching small graphs to large graphs is correct or not. We also show that with some restrictions, the methodology returns the optimal GED in a quadratic time and that it can also be used to generate graph databases to test exact sub-graph isomorphism algorithms.
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Guo, Zhiwei, Hajo Broersma, Ruonan Li, and Shenggui Zhang. "Some algorithmic results for finding compatible spanning circuits in edge-colored graphs." Journal of Combinatorial Optimization 40, no. 4 (September 4, 2020): 1008–19. http://dx.doi.org/10.1007/s10878-020-00644-7.
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Abstract A compatible spanning circuit in a (not necessarily properly) edge-colored graph G is a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. Sufficient conditions for the existence of extremal compatible spanning circuits (i.e., compatible Hamilton cycles and Euler tours), and polynomial-time algorithms for finding compatible Euler tours have been considered in previous literature. More recently, sufficient conditions for the existence of more general compatible spanning circuits in specific edge-colored graphs have been established. In this paper, we consider the existence of (more general) compatible spanning circuits from an algorithmic perspective. We first show that determining whether an edge-colored connected graph contains a compatible spanning circuit is an NP-complete problem. Next, we describe two polynomial-time algorithms for finding compatible spanning circuits in edge-colored complete graphs. These results in some sense give partial support to a conjecture on the existence of compatible Hamilton cycles in edge-colored complete graphs due to Bollobás and Erdős from the 1970s.
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Kim, Jaehyeon, Sejong Lee, Yushin Kim, Seyoung Ahn, and Sunghyun Cho. "Graph Learning-Based Blockchain Phishing Account Detection with a Heterogeneous Transaction Graph." Sensors 23, no. 1 (January 1, 2023): 463. http://dx.doi.org/10.3390/s23010463.
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Recently, cybercrimes that exploit the anonymity of blockchain are increasing. They steal blockchain users’ assets, threaten the network’s reliability, and destabilize the blockchain network. Therefore, it is necessary to detect blockchain cybercriminal accounts to protect users’ assets and sustain the blockchain ecosystem. Many studies have been conducted to detect cybercriminal accounts in the blockchain network. They represented blockchain transaction records as homogeneous transaction graphs that have a multi-edge. They also adopted graph learning algorithms to analyze transaction graphs. However, most graph learning algorithms are not efficient in multi-edge graphs, and homogeneous graphs ignore the heterogeneity of the blockchain network. In this paper, we propose a novel heterogeneous graph structure called an account-transaction graph, ATGraph. ATGraph represents a multi-edge as single edges by considering transactions as nodes. It allows graph learning more efficiently by eliminating multi-edges. Moreover, we compare the performance of ATGraph with homogeneous transaction graphs in various graph learning algorithms. The experimental results demonstrate that the detection performance using ATGraph as input outperforms that using homogeneous graphs as the input by up to 0.2 AUROC.
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RAJASEKARAN, SANGUTHEVAR, and VAMSI KUNDETI. "SPECTRUM BASED TECHNIQUES FOR GRAPH ISOMORPHISM." International Journal of Foundations of Computer Science 20, no. 03 (June 2009): 479–99. http://dx.doi.org/10.1142/s0129054109006693.
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The graph isomorphism problem is to check if two given graphs are isomorphic. Graph isomorphism is a well studied problem and numerous algorithms are available for its solution. In this paper we present algorithms for graph isomorphism that employ the spectra of graphs. An open problem that has fascinated many a scientist is if there exists a polynomial time algorithm for graph isomorphism. Though we do not solve this problem in this paper, the algorithms we present take polynomial time. These algorithms have been tested on a good collection of instances. However, we have not been able to prove that our algorithms will work on all possible instances. In this paper, we also give a new construction for cospectral graphs.
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Korpelainen, Nicholas, Vadim V. Lozin, Dmitriy S. Malyshev, and Alexander Tiskin. "Boundary properties of graphs for algorithmic graph problems." Theoretical Computer Science 412, no. 29 (July 2011): 3545–54. http://dx.doi.org/10.1016/j.tcs.2011.03.001.
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Alrowaili, Dalal Awadh, Uzma Ahmad, Saira Hameeed, and Muhammad Javaid. "Graphs with mixed metric dimension three and related algorithms." AIMS Mathematics 8, no. 7 (2023): 16708–23. http://dx.doi.org/10.3934/math.2023854.
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<abstract><p>Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $. A subset $ S\subseteq V(G) $ is a mixed metric resolving set for $ G $ if every two elements of $ G $ are resolved by some vertex of $ S $. A set of smallest cardinality of mixed metric generator for $ G $ is called the mixed metric dimension. In this paper trees and unicyclic graphs having mixed dimension three are classified. The main aim is to investigate the structure of a simple connected graph having mixed dimension three with respect to the order of graph, maximum degree of basis elements and distance partite sets of basis elements. In particular to find necessary and sufficient conditions for a graph to have mixed metric dimension 3. Moreover three separate algorithms are developed for trees, unicyclic graphs and in general for simple connected graph $ J_{n}\ncong P_{n} $ with $ n\geq 3 $ to determine "whether these graphs have mixed dimension three or not?". If these graphs have mixed dimension three, then these algorithms provide a mixed basis of an input graph.</p></abstract>
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Tang, Jingtao, and Hang Ma. "Large-Scale Multi-Robot Coverage Path Planning via Local Search (Extended Abstract)." Proceedings of the International Symposium on Combinatorial Search 17 (June 1, 2024): 291–92. http://dx.doi.org/10.1609/socs.v17i1.31586.
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We study graph-based Multi-Robot Coverage Path Planning (MCPP) that aims to compute paths for multiple robots to cover all vertices of a given 2D grid terrain graph G. Existing graph-based MCPP algorithms rely on computing a tree cover on G and then employ the Spanning Tree Coverage (STC) paradigm to generate coverage paths on the decomposed graph D of G. In this paper, we take a different approach by exploring how to systematically search for good coverage paths directly on D. We introduce a new algorithmic framework, called LS-MCPP, which leverages a local search to operate directly on D. We propose ESTC, that extends STC to achieve complete coverage for MCPP on any decomposed graphs, even those resulting from incomplete terrain graphs. Furthermore, we demonstrate how to integrate ESTC with three novel types of neighborhood operators into our framework to effectively guide its search process. Remarkably, LS-MCPP scales efficiently to handle MCPP instances with 32 robots on terrain graphs with 11,892 vertices with just minutes of runtime, thereby showcasing its significant benefits for large-scale real-world coverage tasks.
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Grigoriev, Alexander, Bert Marchal, and Natalya Usotskaya. "A Note on the Minimum H-Subgraph Edge Deletion." International Journal of Foundations of Computer Science 26, no. 03 (April 2015): 399–411. http://dx.doi.org/10.1142/s0129054115500227.
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In this note we consider the following problem: Given a graph [Formula: see text] and a subgraph [Formula: see text], what is the smallest subset [Formula: see text] of edges in [Formula: see text] that needs to be deleted from the graph to make it [Formula: see text]-free? Several algorithmic results are presented. First, using the general framework of Courcelle [9], we show that, for a fixed subgraph [Formula: see text], the problem can be solved in linear time on graphs of bounded treewidth. It is known that the constant hidden in the big-O notation of Courcelle algorithm is big which makes the approach impractical. Thus, we present two explicit linear time dynamic programming algorithms on graphs of bounded treewidth for restricted settings of the problem with reasonable constants. Third, using the linear time algorithm for graphs of bounded treewidth, we design a Baker's type polynomial time approximation scheme for the problem on planar graphs.
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Saeed, Ayesha, Ali Husnain, Anam Zahoor, and Mehmood Gondal. "A Comparative Study of Cat Swarm Algorithm for Graph Coloring Problem: Convergence Analysis and Performance Evaluation." International Journal of Innovative Research in Computer Science and Technology 12, no. 4 (July 2024): 1–9. http://dx.doi.org/10.55524/ijircst.2024.12.4.1.
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The Graph Coloring Problem (GCP) is a significant optimization challenge widely suitable to solve scheduling problems. Its goal is to specify the minimum colors (k) required to color a graph properly. Due to its NP-completeness, exact algorithms become impractical for graphs exceeding 100 vertices. As a result, approximation algorithms have gained prominence for tackling large-scale instances. In this context, the Cat Swarm algorithm, a novel population-based metaheuristic in the domain of swarm intelligence, has demonstrated promising convergence properties compared to other population-based algorithms. This research focuses on designing and implementing the Cat Swarm algorithm to address the GCP. By conducting a comparative study with established algorithms, our investigation revolves around quantifying the minimum value of k required by the Cat Swarm algorithm for each graph instance. The evaluation metrics include the algorithm's running time in seconds, success rate, and the mean count of iterations or assessments required to reach a goal.
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Bera, Abhijit, Mrinal Kanti Ghose, and Dibyendu Kumar Pal. "Graph Classification Using Back Propagation Learning Algorithms." International Journal of Systems and Software Security and Protection 11, no. 2 (July 2020): 1–12. http://dx.doi.org/10.4018/ijsssp.2020070101.
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Due to the propagation of graph data, there has been a sharp focus on developing effective methods for classifying the graph object. As most of the proposed graph classification techniques though effective are constrained by high computational overhead, there is a consistent effort to improve upon the existing classification algorithms in terms of higher accuracy and less computational time. In this paper, an attempt has been made to classify graphs by extracting various features and selecting the important features using feature selection algorithms. Since all the extracted graph-based features need not be equally important, only the most important features are selected by using back propagation learning algorithm. The results of the proposed study of feature-based approach using back propagation learning algorithm lead to higher classification accuracy with faster computational time in comparison to other graph kernels. It also appears to be more effective for large unlabeled graphs.
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Terra-Neves, Miguel, José Amaral, Alexandre Lemos, Rui Quintino, Pedro Resende, and Antonio Alegria. "SAT-Based Algorithms for Regular Graph Pattern Matching." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (March 24, 2024): 8136–45. http://dx.doi.org/10.1609/aaai.v38i8.28653.
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Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset.
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Schab, Esteban, Carla Casanova, and Fabiana Piccoli. "Graph Representations for Reinforcement Learning." Journal of Computer Science and Technology 24, no. 1 (April 22, 2024): e03. http://dx.doi.org/10.24215/16666038.24.e03.
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Graph analysis is becoming increasingly important due to the expressive power of graph models and the efficient algorithms available for processing them. Reinforcement Learning is one domain that could benefit from advancements in graph analysis, given that a learning agent may be integrated into an environment that can be represented as a graph. Nevertheless, the structural irregularity of graphs and the lack of prior labels make it difficult to integrate such a model into modern Reinforcement Learning frameworks that rely on artificial neural networks. Graph embedding enables the learning of low-dimensional vector representations that are more suited for machine learning algorithms, while retaining essential graph features. This paper presents a framework for evaluating graph embedding algorithms and their ability to preserve the structure and relevant features of graphs by means of an internal validation metric, without resorting to subsequent tasks that require labels for training. Based on this framework, three defined algorithms that meet the necessary requirements for solving a specific problem of Reinforcement Learning in graphs are selected, analyzed, and compared. These algorithms are Graph2Vec, GL2Vec, and Wavelet Characteristics, with the latter two demonstrating superior performance.
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Şeker, Oylum, Pinar Heggernes, Tinaz Ekim, and Z. Caner Taşkın. "Generation of random chordal graphs using subtrees of a tree." RAIRO - Operations Research 56, no. 2 (March 2022): 565–82. http://dx.doi.org/10.1051/ro/2022027.
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Chordal graphs form one of the most studied graph classes. Several graph problems that are NP-hard in general become solvable in polynomial time on chordal graphs, whereas many others remain NP-hard. For a large group of problems among the latter, approximation algorithms, parameterized algorithms, and algorithms with moderately exponential or sub-exponential running time have been designed. Chordal graphs have also gained increasing interest during the recent years in the area of enumeration algorithms. Being able to test these algorithms on instances of chordal graphs is crucial for understanding the concepts of tractability of hard problems on graph classes. Unfortunately, only few published papers give algorithms for generating chordal graphs. Even in these papers, only very few methods aim for generating a large variety of chordal graphs. Surprisingly, none of these methods is directly based on the “intersection of subtrees of a tree” characterization of chordal graphs. In this paper, we give an algorithm for generating chordal graphs, based on the characterization that a graph is chordal if and only if it is the intersection graph of subtrees of a tree. Upon generating a random host tree, we give and test various methods that generate subtrees of the host tree. We compare our methods to one another and to existing ones for generating chordal graphs. Our experiments show that one of our methods is able to generate the largest variety of chordal graphs in terms of maximal clique sizes. Moreover, two of our subtree generation methods result in an overall complexity of our generation algorithm that is the best possible time complexity for a method generating the entire node set of subtrees in an “intersection of subtrees of a tree” representation. The instances corresponding to the results presented in this paper, and also a set of relatively small-sized instances are made available online.
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Reba, Kristjan, Matej Guid, Kati Rozman, Dušanka Janežič, and Janez Konc. "Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning." Mathematics 10, no. 1 (December 28, 2021): 97. http://dx.doi.org/10.3390/math10010097.
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Finding a maximum clique is important in research areas such as computational chemistry, social network analysis, and bioinformatics. It is possible to compare the maximum clique size between protein graphs to determine their similarity and function. In this paper, improvements based on machine learning (ML) are added to a dynamic algorithm for finding the maximum clique in a protein graph, Maximum Clique Dynamic (MaxCliqueDyn; short: MCQD). This algorithm was published in 2007 and has been widely used in bioinformatics since then. It uses an empirically determined parameter, Tlimit, that determines the algorithm’s flow. We have extended the MCQD algorithm with an initial phase of a machine learning-based prediction of the Tlimit parameter that is best suited for each input graph. Such adaptability to graph types based on state-of-the-art machine learning is a novel approach that has not been used in most graph-theoretic algorithms. We show empirically that the resulting new algorithm MCQD-ML improves search speed on certain types of graphs, in particular molecular docking graphs used in drug design where they determine energetically favorable conformations of small molecules in a protein binding site. In such cases, the speed-up is twofold.
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RIESEN, KASPAR, and HORST BUNKE. "GRAPH CLASSIFICATION BASED ON VECTOR SPACE EMBEDDING." International Journal of Pattern Recognition and Artificial Intelligence 23, no. 06 (September 2009): 1053–81. http://dx.doi.org/10.1142/s021800140900748x.
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Graphs provide us with a powerful and flexible representation formalism for pattern classification. Many classification algorithms have been proposed in the literature. However, the vast majority of these algorithms rely on vectorial data descriptions and cannot directly be applied to graphs. Recently, a growing interest in graph kernel methods can be observed. Graph kernels aim at bridging the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. In the present paper, we propose an approach transforming graphs into n-dimensional real vectors by means of prototype selection and graph edit distance computation. This approach allows one to build graph kernels in a straightforward way. It is not only applicable to graphs, but also to other kind of symbolic data in conjunction with any kind of dissimilarity measure. Thus it is characterized by a high degree of flexibility. With several experimental results, we prove the robustness and flexibility of our new method and show that our approach outperforms other graph classification methods on several graph data sets of diverse nature.
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GIBERT, JAUME, ERNEST VALVENY, and HORST BUNKE. "EMBEDDING OF GRAPHS WITH DISCRETE ATTRIBUTES VIA LABEL FREQUENCIES." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 03 (May 2013): 1360002. http://dx.doi.org/10.1142/s0218001413600021.
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Graph-based representations of patterns are very flexible and powerful, but they are not easily processed due to the lack of learning algorithms in the domain of graphs. Embedding a graph into a vector space solves this problem since graphs are turned into feature vectors and thus all the statistical learning machinery becomes available for graph input patterns. In this work we present a new way of embedding discrete attributed graphs into vector spaces using node and edge label frequencies. The methodology is experimentally tested on graph classification problems, using patterns of different nature, and it is shown to be competitive to state-of-the-art classification algorithms for graphs, while being computationally much more efficient.
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Paul, Kaustav, and Arti Pandey. "Some Algorithmic Results for Eternal Vertex Cover Problem in Graphs." Journal of Graph Algorithms and Applications 28, no. 3 (September 10, 2024): 69–85. http://dx.doi.org/10.7155/jgaa.v28i3.2972.
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The eternal vertex cover problem is a variant of the vertex cover problem. It is a two-player (attacker and defender) game in which, given a graph $G=(V,E)$, the defender needs to allocate guards at some vertices so that the allocated vertices form a vertex cover. The attacker can attack one edge at a time, and the defender needs to move the guards along the edges such that at least one guard moves through the attacked edge and the new configuration still remains a vertex cover. The attacker wins if no such move exists for the defender. The defender wins if there exists a strategy to defend the graph against infinite sequence of attacks. The minimum number of guards with which the defender can form a winning strategy is called the eternal vertex cover number of $G$, and is denoted by $evc(G)$. Given a graph $G$, the problem of finding the eternal vertex cover number is NP-hard for general graphs and remains NP-hard even for bipartite graphs. We have given a polynomial time algorithm to find the Eternal vertex cover number in chain graphs and $P_4$-sparse graphs. We have also given a linear-time algorithm to find the eternal vertex cover number for split graphs, an important subclass of chordal graphs.
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Kamath, S. S., A. Senthil Thilak, and M. Rashmi. "Algorithmic aspects of k-part degree restricted domination in graphs." Discrete Mathematics, Algorithms and Applications 12, no. 05 (July 7, 2020): 2050057. http://dx.doi.org/10.1142/s1793830920500573.
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The concept of network is predominantly used in several applications of computer communication networks. It is also a fact that the dominating set acts as a virtual backbone in a communication network. These networks are vulnerable to breakdown due to various causes, including traffic congestion. In such an environment, it is necessary to regulate the traffic so that these vulnerabilities could be reasonably controlled. Motivated by this, [Formula: see text]-part degree restricted domination is defined as follows. For a positive integer [Formula: see text], a dominating set [Formula: see text] of a graph [Formula: see text] is said to be a [Formula: see text]-part degree restricted dominating set ([Formula: see text]-DRD set) if for all [Formula: see text], there exists a set [Formula: see text] such that [Formula: see text] and [Formula: see text]. The minimum cardinality of a [Formula: see text]-DRD set of a graph [Formula: see text] is called the [Formula: see text]-part degree restricted domination number of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we present a polynomial time reduction that proves the NP -completeness of the [Formula: see text]-part degree restricted domination problem for bipartite graphs, chordal graphs, undirected path graphs, chordal bipartite graphs, circle graphs, planar graphs and split graphs. We propose a polynomial time algorithm to compute a minimum [Formula: see text]-DRD set of a tree and minimal [Formula: see text]-DRD set of a graph.
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Theodorakopoulos, Leonidas, Aristeidis Karras, Alexandra Theodoropoulou, and Georgios Kampiotis. "Benchmarking Big Data Systems: Performance and Decision-Making Implications in Emerging Technologies." Technologies 12, no. 11 (November 3, 2024): 217. http://dx.doi.org/10.3390/technologies12110217.
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Systems for graph processing are a key enabler for insights from large-scale graphs that are critical to many new advanced technologies such as Artificial Intelligence, Internet of Things, and blockchain. In this study, we benchmark another two widely utilized graph processing systems, Apache Spark GraphX and Apache Fink, concerning the key performance criterion by means of response time, scalability, and computational complexity. We demonstrate our results which show the capability of each system for real-world graph applications, and hence, providing a quantitative understanding to select the system for our purpose. GraphX’s strength was in processing batch in-memory workloads typical of blockchain and machine learning model optimization, while Flink excelled in processing stream data, which is timely and important to the IoT world. These performance characteristics emphasize how the capabilities of graph processing systems can match the requirements for the performance of different emerging technology applications. Our findings ultimately inform practitioners about system efficiencies and limitations, but also the recent advances in hardware accelerators and algorithmic improvements aimed at shaping the new graph processing frontier in diverse technology domains.
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Shiokawa, Hiroaki, and Yasunori Futamura. "Efficient Vector Partitioning Algorithms for Graph Clustering." Journal of Data Intelligence 1, no. 2 (June 2020): 101–23. http://dx.doi.org/10.26421/jdi1.2-1.
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This paper addressed the problem of finding clusters included in graph-structured data such as Web graphs, social networks, and others. Graph clustering is one of the fundamental techniques for understanding structures present in the complex graphs such as Web pages, social networks, and others. In the Web and data mining communities, the modularity-based graph clustering algorithm is successfully used in many applications. However, it is difficult for the modularity-based methods to find fine-grained clusters hidden in large-scale graphs; the methods fail to reproduce the ground truth. In this paper, we present a novel modularity-based algorithm, \textit{CAV}, that shows better clustering results than the traditional algorithm. The proposed algorithm employs a cohesiveness-aware vector partitioning into the graph spectral analysis to improve the clustering accuracy. Additionally, this paper also presents a novel efficient algorithm \textit{P-CAV} for further improving the clustering speed of CAV; P-CAV is an extension of CAV that utilizes the thread-based parallelization on a many-core CPU. Our extensive experiments on synthetic and public datasets demonstrate the performance superiority of our approaches over the state-of-the-art approaches.