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Relevant bibliographies by topics / Random weighted graphs

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Academic literature on the topic 'Random weighted graphs'

Author: Grafiati

Published: 14 December 2024

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Journal articles on the topic "Random weighted graphs"

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Komjáthy, Júlia, and Bas Lodewijks. "Explosion in weighted hyperbolic random graphs and geometric inhomogeneous random graphs." Stochastic Processes and their Applications 130, no. 3 (March 2020): 1309–67. http://dx.doi.org/10.1016/j.spa.2019.04.014.

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Vengerovsky, V. "Eigenvalue Distribution of Bipartite Large Weighted Random Graphs. Resolvent Approach." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 1 (March 25, 2016): 78–93. http://dx.doi.org/10.15407/mag12.01.078.

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Davis, Michael, Zhanyu Ma, Weiru Liu, Paul Miller, Ruth Hunter, and Frank Kee. "Generating Realistic Labelled, Weighted Random Graphs." Algorithms 8, no. 4 (December 8, 2015): 1143–74. http://dx.doi.org/10.3390/a8041143.

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Amini, Hamed, Moez Draief, and Marc Lelarge. "Flooding in Weighted Sparse Random Graphs." SIAM Journal on Discrete Mathematics 27, no. 1 (January 2013): 1–26. http://dx.doi.org/10.1137/120865021.

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Amini, Hamed, and Marc Lelarge. "The diameter of weighted random graphs." Annals of Applied Probability 25, no. 3 (June 2015): 1686–727. http://dx.doi.org/10.1214/14-aap1034.

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Ganesan, Ghurumuruhan. "Weighted Eulerian extensions of random graphs." Gulf Journal of Mathematics 16, no. 2 (April 12, 2024): 1–11. http://dx.doi.org/10.56947/gjom.v16i2.1866.

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The Eulerian extension number of any graph H (i.e. the minimum number of edges needed to be added to make H Eulerian) is at least t(H), half the number of odd degree vertices of H. In this paper we consider weighted Eulerian extensions of a random graph G where we add edges of bounded weights and use an iterative probabilistic method to obtain sufficient conditions for the weighted Eulerian extension number of G to grow linearly with t(G). We derive our conditions in terms of the average edge probabilities and edge density and also show that bounded extensions are rare by estimating the skewness of a fixed weighted extension. Finally, we briefly describe a decomposition involving Eulerian extensions of G to convert a large dataset into small dissimilar batches.

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Porfiri, Maurizio, and Daniel J. Stilwell. "Consensus Seeking Over Random Weighted Directed Graphs." IEEE Transactions on Automatic Control 52, no. 9 (September 2007): 1767–73. http://dx.doi.org/10.1109/tac.2007.904603.

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Khorunzhy, O., M. Shcherbina, and V. Vengerovsky. "Eigenvalue distribution of large weighted random graphs." Journal of Mathematical Physics 45, no. 4 (April 2004): 1648–72. http://dx.doi.org/10.1063/1.1667610.

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Mountford, Thomas, and Jacques Saliba. "Flooding and diameter in general weighted random graphs." Journal of Applied Probability 57, no. 3 (September 2020): 956–80. http://dx.doi.org/10.1017/jpr.2020.45.

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AbstractIn this paper we study first passage percolation on a random graph model, the configuration model. We first introduce the notions of weighted diameter, which is the maximum of the weighted lengths of all optimal paths between any two vertices in the graph, and the flooding time, which represents the time (weighted length) needed to reach all the vertices in the graph starting from a uniformly chosen vertex. Our result consists in describing the asymptotic behavior of the diameter and the flooding time, as the number of vertices n tends to infinity, in the case where the weight distribution G has an exponential tail behavior, and proving that this category of distributions is the largest possible for which the asymptotic behavior holds.

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Mosbah, M., and N. Saheb. "Non-uniform random spanning trees on weighted graphs." Theoretical Computer Science 218, no. 2 (May 1999): 263–71. http://dx.doi.org/10.1016/s0304-3975(98)00325-9.

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Dissertations / Theses on the topic "Random weighted graphs"

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Davidson, Angus William. "Scaling properties of optimisation problems on random weighted graphs." Thesis, University of Bristol, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752771.

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Gabrysch, Katja. "On Directed Random Graphs and Greedy Walks on Point Processes." Doctoral thesis, Uppsala universitet, Analys och sannolikhetsteori, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-305859.

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This thesis consists of an introduction and five papers, of which two contribute to the theory of directed random graphs and three to the theory of greedy walks on point processes. We consider a directed random graph on a partially ordered vertex set, with an edge between any two comparable vertices present with probability p, independently of all other edges, and each edge is directed from the vertex with smaller label to the vertex with larger label. In Paper I we consider a directed random graph on ℤ2 with the vertices ordered according to the product order and we show that the limiting distribution of the centered and rescaled length of the longest path from (0,0) to (n, [na] ), a<3/14, is the Tracy-Widom distribution. In Paper II we show that, under a suitable rescaling, the closure of vertex 0 of a directed random graph on ℤ with edge probability n−1 converges in distribution to the Poisson-weighted infinite tree. Moreover, we derive limit theorems for the length of the longest path of the Poisson-weighted infinite tree. The greedy walk is a deterministic walk on a point process that always moves from its current position to the nearest not yet visited point. Since the greedy walk on a homogeneous Poisson process on the real line, starting from 0, almost surely does not visit all points, in Paper III we find the distribution of the number of visited points on the negative half-line and the distribution of the index at which the walk achieves its minimum. In Paper IV we place homogeneous Poisson processes first on two intersecting lines and then on two parallel lines and we study whether the greedy walk visits all points of the processes. In Paper V we consider the greedy walk on an inhomogeneous Poisson process on the real line and we determine sufficient and necessary conditions on the mean measure of the process for the walk to visit all points.

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Russ, Ricardo. "Service Level Achievments - Test Data for Optimal Service Selection." Thesis, Linnéuniversitetet, Institutionen för datavetenskap (DV), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-50538.

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This bachelor’s thesis was written in the context of a joint research group, which developed a framework for finding and providing the best-fit web service for a user. The problem of the research group lays in testing their developed framework sufficiently. The framework can either be tested with test data produced by real web services which costs money or by generated test data based on a simulation of web service behavior. The second attempt has been developed within this scientific paper in the form of a test data generator. The generator simulates a web service request by defining internal services, whereas each service has an own internal graph which considers the structure of a service. A service can be atomic or can be compose of other services that are called in a specific manner (sequential, loop, conditional). The generation of the test data is done by randomly going through the services which result in variable response times, since the graph structure changes every time the system has been initialized. The implementation process displayed problems which have not been solved within the time frame. Those problems are displaying interesting challenges for the dynamical generation of random graphs. Those challenges should be targeted in further research.

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Weibel, Julien. "Graphons de probabilités, limites de graphes pondérés aléatoires et chaînes de Markov branchantes cachées." Electronic Thesis or Diss., Orléans, 2024. http://www.theses.fr/2024ORLE1031.

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Les graphes sont des objets mathématiques qui servent à modéliser tout type de réseaux, comme les réseaux électriques, les réseaux de communications et les réseaux sociaux. Formellement un graphe est composé d'un ensemble de sommets et d'un ensemble d'arêtes reliant des paires de sommets. Les sommets représentent par exemple des individus, tandis que les arêtes représentent les interactions entre ces individus. Dans le cas d'un graphe pondéré, chaque arête possède un poids ou une décoration pouvant modéliser une distance, une intensité d'interaction, une résistance. La modélisation de réseaux réels fait souvent intervenir de grands graphes qui ont un grand nombre de sommets et d'arêtes.La première partie de cette thèse est consacrée à l'introduction et à l'étude des propriétés des objets limites des grands graphes pondérés : les graphons de probabilités. Ces objets sont une généralisation des graphons introduits et étudiés par Lovász et ses co-auteurs dans le cas des graphes sans poids sur les arêtes. À partir d'une distance induisant la topologie faible sur les mesures, nous définissons une distance de coupe sur les graphons de probabilités. Nous exhibons un critère de tension pour les graphons de probabilités lié à la compacité relative dans la distance de coupe. Enfin, nous prouvons que cette topologie coïncide avec la topologie induite par la convergence en distribution des sous-graphes échantillonnés. Dans la deuxième partie de cette thèse, nous nous intéressons aux modèles markoviens cachés indexés par des arbres. Nous montrons la consistance forte et la normalité asymptotique de l'estimateur de maximum de vraisemblance pour ces modèles sous des hypothèses standards. Nous montrons un théorème ergodique pour des chaînes de Markov branchantes indexés par des arbres avec des formes générales. Enfin, nous montrons que pour une chaîne stationnaire et réversible, le graphe ligne est la forme d'arbre induisant une variance minimale pour l'estimateur de moyenne empirique parmi les arbres avec un nombre donné de sommets
Graphs are mathematical objects used to model all kinds of networks, such as electrical networks, communication networks, and social networks. Formally, a graph consists of a set of vertices and a set of edges connecting pairs of vertices. The vertices represent, for example, individuals, while the edges represent the interactions between these individuals. In the case of a weighted graph, each edge has a weight or a decoration that can model a distance, an interaction intensity, or a resistance. Modeling real-world networks often involves large graphs with a large number of vertices and edges.The first part of this thesis is dedicated to introducing and studying the properties of the limit objects of large weighted graphs : probability-graphons. These objects are a generalization of graphons introduced and studied by Lovász and his co-authors in the case of unweighted graphs. Starting from a distance that induces the weak topology on measures, we define a cut distance on probability-graphons. We exhibit a tightness criterion for probability-graphons related to relative compactness in the cut distance. Finally, we prove that this topology coincides with the topology induced by the convergence in distribution of the sampled subgraphs. In the second part of this thesis, we focus on hidden Markov models indexed by trees. We show the strong consistency and asymptotic normality of the maximum likelihood estimator for these models under standard assumptions. We prove an ergodic theorem for branching Markov chains indexed by trees with general shapes. Finally, we show that for a stationary and reversible chain, the line graph is the tree shape that induces the minimal variance for the empirical mean estimator among trees with a given number of vertices

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Caetano, Tiberio Silva. "Graphical models and point set matching." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2004. http://hdl.handle.net/10183/4041.

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Casamento de padrões de pontos em Espaços Euclidianos é um dos problemas fundamentais em reconhecimento de padrões, tendo aplicações que vão desde Visão Computacional até Química Computacional. Sempre que dois padrões complexos estão codi- ficados em termos de dois conjuntos de pontos que identificam suas características fundamentais, sua comparação pode ser vista como um problema de casamento de padrões de pontos. Este trabalho propõe uma abordagem unificada para os problemas de casamento exato e inexato de padrões de pontos em Espaços Euclidianos de dimensão arbitrária. No caso de casamento exato, é garantida a obtenção de uma solução ótima. Para casamento inexato (quando ruído está presente), resultados experimentais confirmam a validade da abordagem. Inicialmente, considera-se o problema de casamento de padrões de pontos como um problema de casamento de grafos ponderados. O problema de casamento de grafos ponderados é então formulado como um problema de inferência Bayesiana em um modelo gráfico probabilístico. Ao explorar certos vínculos fundamentais existentes em padrões de pontos imersos em Espaços Euclidianos, provamos que, para o casamento exato de padrões de pontos, um modelo gráfico simples é equivalente ao modelo completo. É possível mostrar que inferência probabilística exata neste modelo simples tem complexidade polinomial para qualquer dimensionalidade do Espaço Euclidiano em consideração. Experimentos computacionais comparando esta técnica com a bem conhecida baseada em relaxamento probabilístico evidenciam uma melhora significativa de desempenho para casamento inexato de padrões de pontos. A abordagem proposta é signi- ficativamente mais robusta diante do aumento do tamanho dos padrões envolvidos. Na ausência de ruído, os resultados são sempre perfeitos.
Point pattern matching in Euclidean Spaces is one of the fundamental problems in Pattern Recognition, having applications ranging from Computer Vision to Computational Chemistry. Whenever two complex patterns are encoded by two sets of points identifying their key features, their comparison can be seen as a point pattern matching problem. This work proposes a single approach to both exact and inexact point set matching in Euclidean Spaces of arbitrary dimension. In the case of exact matching, it is assured to find an optimal solution. For inexact matching (when noise is involved), experimental results confirm the validity of the approach. We start by regarding point pattern matching as a weighted graph matching problem. We then formulate the weighted graph matching problem as one of Bayesian inference in a probabilistic graphical model. By exploiting the existence of fundamental constraints in patterns embedded in Euclidean Spaces, we prove that for exact point set matching a simple graphical model is equivalent to the full model. It is possible to show that exact probabilistic inference in this simple model has polynomial time complexity with respect to the number of elements in the patterns to be matched. This gives rise to a technique that for exact matching provably finds a global optimum in polynomial time for any dimensionality of the underlying Euclidean Space. Computational experiments comparing this technique with well-known probabilistic relaxation labeling show significant performance improvement for inexact matching. The proposed approach is significantly more robust under augmentation of the sizes of the involved patterns. In the absence of noise, the results are always perfect.

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Weihrauch, Tobias. "Characterizations and Probabilistic Representations of Effective Resistance Metrics." 2019. https://ul.qucosa.de/id/qucosa%3A73920.

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This thesis studies effective resistances of finite and infinite weighted graphs. Classical results state that it is a metric on the set of vertices of the graph and that it can be expressed completely in terms of the graph’s random walk. The first goal of this thesis is to provide a concise and accessible starting point for new scholars interested in the topic. In that spirit, we reproduce existing results and review different approaches to effective resistances using tools from several fields such as linear algebra, probability theory, geometry and functional analysis. The second goal is to characterize which metric spaces are given by the effective resistance of a graph. For the finite case, we begin by reconstructing the associated graph from the effective resistance. This leads to a complete algebraic characterization in terms of triangle inequality defects. A more geometric condition is given by showing that a metric space can only be an effective resistance if its minimal graph realization contains no incomplete cycles. We also show that our algebraic characterization can be applied to the more general theory of resistance forms as defined by Kigami. The third goal of this thesis is to investigate probabilistic representations of effective resistances. Building on the work of Tetali and Barlow, we characterize under which conditions known representations for finite graphs can be extended to infinite graphs.

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Books on the topic "Random weighted graphs"

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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Specific constructions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0009.

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This chapter presents network-generating models which cannot be neatly categorized as growing, nor as defined primarily through a target degree distribution. They are best understood as mechanistic constructions designed to elucidate a particular feature of the network. In the first sub-section, the Watts–Strogatz model is introduced and motivated as a construction to achieve both a high degree of clustering and a low average path length. Geometric graphs, in their Euclidian flavour, are shown to be a natural choice for broadcast networks. The Hyperbolic variant is informally described, because it is known to be a natural space in which to embed hierarchical graphs. Planar graphs have very specific real-world applications, but are extraordinarily challenging to analyze mathematically. Finally, weighted graphs allow for concepts such as traffic to be incorporated into the random graph model.

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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Random graph ensembles. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0003.

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This chapter presents some theoretical tools for defining random graph ensembles systematically via soft or hard topological constraints including working through some properties of the Erdös-Rényi random graph ensemble, which is the simplest non-trivial random graph ensemble where links appear between two nodes with a fixed probability p. The chapter sets out the central representation of graph generation as the result of a discrete-time Markovian stochastic process. This unites the two flavours of graph generation approaches – because they can be viewed as simply moving forwards or backwards through this representation. It is possible to define a random graph by an algorithm, and then calculate the associated stationary probability. The alternative approach is to specify sampling weights and then to construct an algorithm that will have these weights as the stationary probabilities upon convergence.

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Newman, Mark. Mathematics of networks. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805090.003.0006.

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An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

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Book chapters on the topic "Random weighted graphs"

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Walley, Scott K., and Harry H. Tan. "Shortest paths in random weighted graphs." In Lecture Notes in Computer Science, 213–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0030835.

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Broise-Alamichel, Anne, Jouni Parkkonen, and Frédéric Paulin. "Random Walks on Weighted Graphs of Groups." In Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees, 141–54. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18315-8_6.

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Kumagai, Takashi. "Heat Kernel Estimates for Random Weighted Graphs." In Lecture Notes in Mathematics, 59–64. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03152-1_5.

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Dai, Qionghai, and Yue Gao. "Mathematical Foundations of Hypergraph." In Artificial Intelligence: Foundations, Theory, and Algorithms, 19–40. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0185-2_2.

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AbstractIn this chapter, we introduce the mathematical foundations of hypergraph and present the mathematical notations that are used to facilitate deep understanding and analysis of hypergraph structure. A hypergraph is composed of a set of vertices and hyperedges, and it is a generalization of a graph, where a weighted hypergraph quantifies the relative importance of hyperedges or vertices. Hypergraph can also be divided into two main categories, i.e., the undirected hypergraph representation and the directed hypergraph representation. The latter one further divides the vertices in one hyperedge into the source vertex set and the target vertex set to model more complex correlations. Additionally, we discuss the relationship between hypergraph and graph from the perspective of structural transformation and expressive ability. The most intuitive difference between a simple graph and a hypergraph can be observed in the size of order and expression of adjacency. A hypergraph can be converted into a simple graph using clique expansion, star expansion, and line expansion. Moreover, the proof based on random walks and Markov chains establishes the relationship between hypergraphs with edge-independent vertex weights and weighted graphs.

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Dani, Varsha, and Cristopher Moore. "Independent Sets in Random Graphs from the Weighted Second Moment Method." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 472–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22935-0_40.

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Nalam, Chaitanya, and Thatchaphol Saranurak. "Maximal k-Edge-Connected Subgraphs in Weighted Graphs via Local Random Contraction." In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 183–211. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2023. http://dx.doi.org/10.1137/1.9781611977554.ch8.

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Gamarnik, David, Tomasz Nowicki, and Grzegorz Swirszcz. "Maximum Weight Independent Sets and Matchings in Sparse Random Graphs." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 357–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-27821-4_32.

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Ackermann, Hanno, Björn Scheuermann, Tat-Jun Chin, and Bodo Rosenhahn. "Randomly Walking Can Get You Lost: Graph Segmentation with Unknown Edge Weights." In Lecture Notes in Computer Science, 450–63. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14612-6_33.

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Gimadi, E. Kh. "Several Edge-Disjoint Spanning Trees with Given Diameter in a Graph with Random Discrete Edge Weights." In Communications in Computer and Information Science, 281–92. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-48751-4_21.

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Gimadi, Edward Kh, Aleksandr S. Shevyakov, and Alexandr A. Shtepa. "On Asymptotically Optimal Approach for the Problem of Finding Several Edge-Disjoint Spanning Trees of Given Diameter in an Undirected Graph with Random Edge Weights." In Mathematical Optimization Theory and Operations Research, 67–78. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77876-7_5.

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Conference papers on the topic "Random weighted graphs"

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Oren-Loberman, Mor, Vered Paslev, and Wasim Huleihel. "Testing Dependency of Weighted Random Graphs." In 2024 IEEE International Symposium on Information Theory (ISIT), 1263–68. IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619266.

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Amini, Hamed, Moez Draief, and Marc Lelarge. "Flooding in Weighted Random Graphs." In 2011 Proceedings of the Eighth Workshop on Analytic Algorithmics and Combinatorics (ANALCO). Philadelphia, PA: Society for Industrial and Applied Mathematics, 2011. http://dx.doi.org/10.1137/1.9781611973013.1.

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Hero III, Alfred O., and Olivier Michel. "Robust entropy estimation strategies based on edge weighted random graphs." In SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, edited by Ali Mohammad-Djafari. SPIE, 1998. http://dx.doi.org/10.1117/12.323804.

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Coppersmith, D., P. Doyle, P. Raghavan, and M. Snir. "Random walks on weighted graphs, and applications to on-line algorithms." In the twenty-second annual ACM symposium. New York, New York, USA: ACM Press, 1990. http://dx.doi.org/10.1145/100216.100266.

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Larroca, Federico, Paola Bermolen, Marcelo Fiori, and Gonzalo Mateos. "Change Point Detection in Weighted and Directed Random Dot Product Graphs." In 2021 29th European Signal Processing Conference (EUSIPCO). IEEE, 2021. http://dx.doi.org/10.23919/eusipco54536.2021.9616036.

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Kalisky, Tomer. "Scale-Free properties of weighted random graphs: Minimum Spanning Trees and Percolation." In SCIENCE OF COMPLEX NETWORKS: From Biology to the Internet and WWW: CNET 2004. AIP, 2005. http://dx.doi.org/10.1063/1.1985379.

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Cui, Yaxin, Faez Ahmed, Zhenghui Sha, Lijun Wang, Yan Fu, and Wei Chen. "A Weighted Network Modeling Approach for Analyzing Product Competition." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22591.

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Abstract Statistical network models allow us to study the co-evolution between the products and the social aspects of a market system, by modeling these components and their interactions as graphs. In this paper, we study competition between different car models using network theory, with a focus on how product attributes (like fuel economy and price) affect which cars are considered together and which cars are finally bought by customers. Unlike past work, where most systems have been studied with the assumption that relationships between competitors are binary (i.e., whether a relationship exists or not), we allow relationships to take strengths (i.e., how strong a relationship is). Specifically, we use valued Exponential Random Graph Models and show that our approach provides a significant improvement over the baselines in predicting product co-considerations as well as in the validation of market share. This is also the first attempt to study aggregated purchase preference and car competition using valued directed networks.

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Cai, Shaowei, Wenying Hou, Jinkun Lin, and Yuanjie Li. "Improving Local Search for Minimum Weight Vertex Cover by Dynamic Strategies." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/196.

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The minimum weight vertex cover (MWVC) problem is an important combinatorial optimization problem with various real-world applications. Due to its NP hardness, most works on solving MWVC focus on heuristic algorithms that can return a good quality solution in reasonable time. In this work, we propose two dynamic strategies that adjust the behavior of the algorithm during search, which are used to improve a state of the art local search for MWVC named FastWVC, resulting in two local search algorithms called DynWVC1 and DynWVC2. Previous MWVC algorithms are evaluated on graphs with random or hand crafted weights. In this work, we evaluate the algorithms on the vertex weighted graphs that obtained from an important real world problem, the map labeling problem. Experiments show that our algorithm obtains better results than previous algorithms for MWVC and maximum weight independent set (MWIS) on these real world instances. We also test our algorithms on massive graphs studied in previous works, and show significant improvements there.

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Doshi, Vishwaraj, Jie Hu, and Do Young Eun. "Self-Repellent Random Walks on General Graphs - Achieving Minimal Sampling Variance via Nonlinear Markov Chains (Extended Abstract)." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. California: International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/929.

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We consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of Markov chain Monte Carlo (MCMC) procedures. Given any Markov chain corresponding to a target probability distribution, we design a self-repellent random walk (SRRW) which is less likely to transition to nodes that were highly visited in the past, and more likely to transition to seldom visited nodes. For a class of SRRWs parameterized by a positive real α, we prove that the empirical distribution of the process converges almost surely to the target (stationary) distribution of the underlying Markov chain kernel. We then provide a central limit theorem and derive the exact form of the arising asymptotic co-variance matrix, which allows us to show that the SRRW with stronger repellence (larger α) always achieves a smaller asymptotic covariance, in the sense of Loewner ordering of co-variance matrices. Especially for SRRW-driven MCMC algorithms, we show that the decrease in the asymptotic sampling variance is of the order O(1/α), eventually going down to zero. After generalizing these results for a class of weighted empirical measures, we use them as a stepping stone to show that a similar performance ordering can also be obtained for distributed stochastic optimization tasks using token algorithms. More explicitly, by replacing a Markovian token by a SRRW version with the same target distribution, we show that the asymptotic co-variance of the optimization iterates decreases at rate O(1/α^2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.

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Xinyi Chen. "Priority weighted BA random graph model." In 2011 International Conference on Computer Science and Service System (CSSS). IEEE, 2011. http://dx.doi.org/10.1109/csss.2011.5972129.

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Reports on the topic "Random weighted graphs"

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Goetsch, Arthur L., Yoav Aharoni, Arieh Brosh, Ryszard (Richard) Puchala, Terry A. Gipson, Zalman Henkin, Eugene D. Ungar, and Amit Dolev. Energy Expenditure for Activity in Free Ranging Ruminants: A Nutritional Frontier. United States Department of Agriculture, June 2009. http://dx.doi.org/10.32747/2009.7696529.bard.

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Heat production (HP) or energy expenditure for activity (EEa) is of fundamental nutritional importance for livestock because it determines the proportion of ingested nutrients available for productive functions. Previous estimates of EEa are unreliable and vary widely with different indirect methodologies. This leads to erroneous nutritional strategies, especially when intake on pasture does not meet nutritional requirements and supplementation is necessary for acceptable production. Therefore, the objective of this project was to measure EEa in different classes of livestock (beef cattle and goats) over a wide range of ecological and management conditions to develop and evaluate simple means of prediction. In the first study in Israel, small frame (SF) and large frame (LF) cows (268 and 581 kg) were monitored during spring, summer, and autumn. Feed intake by SF cows per unit of metabolic weight was greater (P < 0.001) than that by LF cows in both spring and summer and their apparent selection of higher quality herbage in spring was greater (P < 0.10) than that of LF cows. SF cows grazed more hours per day and walked longer distances than the LF cows during all seasons. The coefficient of specific costs of activities (kJ•kg BW-0.75•d-1) and of locomotion (J•kg BW-0.75•m-1) were smaller for the SF cows. In the second study, cows were monitored in March, May, and September when they grazed relatively large plots, 135 and 78 ha. Energy cost coefficients of standing, grazing, and horizontal locomotion derived were similar to those of the previous study based on data from smaller plots. However, the energy costs of walking idle and of vertical locomotion were greater than those found by Brosh et al. (2006) but similar to those found by Aharoni et al. (2009). In the third study, cows were monitored in February and May in a 78-ha plot with an average slope of 15.5°, whereas average plot slopes of the former studies ranged between 4.3 and 6.9°. Energy cost coefficients of standing, grazing, and walking idle were greater than those calculated in the previous studies. However, the estimated energy costs of locomotion were lower in the steeper plot. A comparison on a similar HP basis, i.e., similar metabolizable energy (ME) intake, shows that the daily energy spent on activities in relation to daily HP increased by 27% as the average plot slope increased from 5.8 and 6.02 to 15.5°. In the fourth study, cows grazing in a woodland habitat were monitored as in previous studies in December, March, and July. Data analysis is in progress. In the first US experiment, Boer and Spanish does with two kids were used in an experiment beginning in late spring at an average of 24 days after kidding. Two does of each breed resided in eight 0.5-ha grass/forb pastures. Periods of 56, 60, 63, 64, and 73 days in length corresponded to mid-lactation, early post-weaning, the late dry period, early gestation, and mid-gestation. EEa expressed as a percentage of the ME requirement for maintenance plus activity in confinement (EEa%) was not influenced by stocking rate, breed, or period, averaging 49%. Behavioral activities (e.g., time spent grazing, walking, and idle, distance traveled) were not highly related to EEa%, although no-intercept regressions against time spent grazing/eating and grazing/eating plus walking indicated an increase in EEa% of 5.8 and 5.1%/h, respectively. In the second study, animal types were yearling Angora doeling goats, yearling Boer wether goats, yearling Spanish wether goats, and Rambouilletwether sheep slightly more than 2 yr of age. Two animals of each type were randomly allocated to one of four pastures 9.3, 12.3, 4.6, and 1.2 ha in area. The experiment was conducted in the summer with three periods, 30, 26, and 26 days in length. EEa% was affected by an interaction between animal type and period (Angora: 16, 17, and 15; Boer: 60, 67, and 34; Spanish: 46, 62, and 42; sheep: 22, 12, and 22% in periods 1, 2, and 3, respectively (SE = 6.1)). EEa% of goats was predicted with moderate accuracy (R2 = 0.40-0.41) and without bias from estimates of 5.8 and 5.1%/h spent grazing/eating and grazing/eating plus walking, respectively, determined in the first experiment; however, these methods were not suitable for sheep. These methods of prediction are simpler and more accurate than currently recommended for goats by the National Research Council.

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