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Journal articles on the topic 'Geometric Intersection Graphs'

Author: Grafiati

Published: 6 September 2023

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1

Fekete, Sándor P., and Phillip Keldenich. "Conflict-Free Coloring of Intersection Graphs." International Journal of Computational Geometry & Applications 28, no. 03 (2018): 289–307. http://dx.doi.org/10.1142/s0218195918500085.

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A conflict-free[Formula: see text]-coloring of a graph [Formula: see text] assigns one of [Formula: see text] different colors to some of the vertices such that, for every vertex [Formula: see text], there is a color that is assigned to exactly one vertex among [Formula: see text] and [Formula: see text]’s neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflict-free coloring of geometric intersection graphs. We demonstrate that the intersection graph of [Formula: see text] geometric objects wit

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2

Baste, Julien, and Dimitrios M. Thilikos. "Contraction Bidimensionality of Geometric Intersection Graphs." Algorithmica 84, no. 2 (2022): 510–31. http://dx.doi.org/10.1007/s00453-021-00912-w.

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3

Eppstein, David. "Testing bipartiteness of geometric intersection graphs." ACM Transactions on Algorithms 5, no. 2 (2009): 1–35. http://dx.doi.org/10.1145/1497290.1497291.

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4

Cabello, Sergio, and Wolfgang Mulzer. "Minimum cuts in geometric intersection graphs." Computational Geometry 94 (March 2021): 101720. http://dx.doi.org/10.1016/j.comgeo.2020.101720.

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5

Uehara, Ryuhei. "Tractabilities and Intractabilities on Geometric Intersection Graphs." Algorithms 6, no. 1 (2013): 60–83. http://dx.doi.org/10.3390/a6010060.

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6

Erlebach, Thomas, and Jiri Fiala. "On-line coloring of geometric intersection graphs." Computational Geometry 23, no. 2 (2002): 243–55. http://dx.doi.org/10.1016/s0925-7721(02)00089-5.

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7

Tokunaga, Shin-ichi. "Intersection number of two connected geometric graphs." Information Processing Letters 59, no. 6 (1996): 331–33. http://dx.doi.org/10.1016/0020-0190(96)00124-x.

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8

Erlebach, Thomas, Klaus Jansen, and Eike Seidel. "Polynomial-Time Approximation Schemes for Geometric Intersection Graphs." SIAM Journal on Computing 34, no. 6 (2005): 1302–23. http://dx.doi.org/10.1137/s0097539702402676.

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9

Agnarsson, Geir, Peter Damaschke, and Magnús M. Halldórsson. "Powers of geometric intersection graphs and dispersion algorithms." Discrete Applied Mathematics 132, no. 1-3 (2003): 3–16. http://dx.doi.org/10.1016/s0166-218x(03)00386-x.

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10

de Berg, Mark, Sándor Kisfaludi-Bak, and Gerhard Woeginger. "The complexity of Dominating Set in geometric intersection graphs." Theoretical Computer Science 769 (May 2019): 18–31. http://dx.doi.org/10.1016/j.tcs.2018.10.007.

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11

Kim, Seog-Jin, and Kittikorn Nakprasit. "Coloring the complements of intersection graphs of geometric figures." Discrete Mathematics 308, no. 20 (2008): 4589–94. http://dx.doi.org/10.1016/j.disc.2007.08.072.

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12

Cabello, Sergio, and Miha Jejčič. "Refining the Hierarchies of Classes of Geometric Intersection Graphs." Electronic Notes in Discrete Mathematics 54 (October 2016): 223–28. http://dx.doi.org/10.1016/j.endm.2016.09.039.

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13

Pawlik, Arkadiusz, Jakub Kozik, Tomasz Krawczyk, et al. "Triangle-Free Geometric Intersection Graphs with Large Chromatic Number." Discrete & Computational Geometry 50, no. 3 (2013): 714–26. http://dx.doi.org/10.1007/s00454-013-9534-9.

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14

Keller, Chaya, and Shakhar Smorodinsky. "Conflict-Free Coloring of Intersection Graphs of Geometric Objects." Discrete & Computational Geometry 64, no. 3 (2019): 916–41. http://dx.doi.org/10.1007/s00454-019-00097-8.

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15

da Fonseca, Guilherme D., Vinícius Gusmão Pereira de Sá, and Celina Miraglia Herrera de Figueiredo. "Shifting Coresets: Obtaining Linear-Time Approximations for Unit Disk Graphs and Other Geometric Intersection Graphs." International Journal of Computational Geometry & Applications 27, no. 04 (2017): 255–76. http://dx.doi.org/10.1142/s0218195917500078.

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Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy that allows us to obtain linear-time constant-factor approximation algorithms for such problems. To illustrate the applicability of the proposed variation, we obtain results for three well-known optimization problems. Among such results, the proposed method yields linear-time [Formula: see text]-approximations for the maximum-weight independent set and the min

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16

Kurniawan, Bayu, Helga Yermadona, and Surya Eka Priana. "EVALUASI SIMPANG TAK BERSINYAL DI SIMPANG LIMAU BUKITTINGGI." Ensiklopedia Research and Community Service Review 1, no. 3 (2022): 20–28. http://dx.doi.org/10.33559/err.v1i3.1232.

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Simpang Limau is one of the Three Unsignalized Intersections on the Bukittinggi-Payakumbuh Cross Road, which has a fairly heavy traffic flow. The purpose of this study was to analyze the performance of an unsignaled intersection using MKJI 1997. The data needed in this study were primary data and secondary data. The primary data is in the form of data on traffic flow conditions, geometric intersections and environmental conditions. Secondary data includes population growth and road network maps. Traffic data collection is carried out by conducting a direct survey to the location for three days

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17

Walczak, Bartosz. "Triangle-Free Geometric Intersection Graphs with No Large Independent Sets." Discrete & Computational Geometry 53, no. 1 (2014): 221–25. http://dx.doi.org/10.1007/s00454-014-9645-y.

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18

BEREG, SERGEY, ADRIAN DUMITRESCU, and MINGHUI JIANG. "MAXIMUM AREA INDEPENDENT SETS IN DISK INTERSECTION GRAPHS." International Journal of Computational Geometry & Applications 20, no. 02 (2010): 105–18. http://dx.doi.org/10.1142/s0218195910003220.

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Maximum Independent Set (MIS) and its relative Maximum Weight Independent Set (MWIS) are well-known problems in combinatorial optimization; they are NP-hard even in the geometric setting of unit disk graphs. In this paper, we study the Maximum Area Independent Set (MAIS) problem, a natural restricted version of MWIS in disk intersection graphs where the weight equals the disk area. We obtain: (i) Quantitative bounds on the maximum total area of an independent set relative to the union area; (ii) Practical constant-ratio approximation algorithms for finding an independent set with a large total

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19

Fox, Jacob, and János Pach. "Coloring Kk-free intersection graphs of geometric objects in the plane." European Journal of Combinatorics 33, no. 5 (2012): 853–66. http://dx.doi.org/10.1016/j.ejc.2011.09.021.

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20

Iyer, Srikanth K., and D. Yogeshwaran. "Percolation and Connectivity in AB Random Geometric Graphs." Advances in Applied Probability 44, no. 1 (2012): 21–41. http://dx.doi.org/10.1239/aap/1331216643.

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Given two independent Poisson point processes Φ(1), Φ(2) in , the AB Poisson Boolean model is the graph with the points of Φ(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Φ(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d ≥ 2 and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poi

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21

Iyer, Srikanth K., and D. Yogeshwaran. "Percolation and Connectivity in AB Random Geometric Graphs." Advances in Applied Probability 44, no. 01 (2012): 21–41. http://dx.doi.org/10.1017/s0001867800005437.

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Given two independent Poisson point processes Φ(1), Φ(2) in , the AB Poisson Boolean model is the graph with the points of Φ(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Φ(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d ≥ 2 and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poi

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22

De, Minati, Subhas C. Nandy, and Sasanka Roy. "In-place algorithms for computing a largest clique in geometric intersection graphs." Discrete Applied Mathematics 178 (December 2014): 58–70. http://dx.doi.org/10.1016/j.dam.2014.06.025.

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23

Böltz, Lucas, and Hannes Frey. "Automatically Testing Containedness between Geometric Graph Classes Defined by Inclusion, Exclusion, and Transfer Axioms under Simple Transformations." Information 13, no. 12 (2022): 578. http://dx.doi.org/10.3390/info13120578.

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We study classes of geometric graphs, which all correspond to the following structural characteristic. For each instance of a vertex set drawn from a universe of possible vertices, each pair of vertices is either required to be connected, forbidden to be connected, or existence or non-existence of an edge is undetermined. The conditions which require or forbid edges are universally quantified predicates defined over the vertex pair, and optionally over existence or non-existence of another edge originating at the vertex pair. We consider further a set of simple graph transformations, where the

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24

de Berg, Mark, Hans L. Bodlaender, Sándor Kisfaludi-Bak, Dániel Marx, and Tom C. van der Zanden. "A Framework for Exponential-Time-Hypothesis--Tight Algorithms and Lower Bounds in Geometric Intersection Graphs." SIAM Journal on Computing 49, no. 6 (2020): 1291–331. http://dx.doi.org/10.1137/20m1320870.

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25

Soroko, Ignat. "Realizable ranks of joins and intersections of subgroups in free groups." International Journal of Algebra and Computation 30, no. 03 (2019): 625–66. http://dx.doi.org/10.1142/s0218196720500149.

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The famous Hanna Neumann Conjecture (now the Friedman–Mineyev theorem) gives an upper bound for the ranks of the intersection of arbitrary subgroups [Formula: see text] and [Formula: see text] of a non-abelian free group. It is an interesting question to “quantify” this bound with respect to the rank of [Formula: see text], the subgroup generated by [Formula: see text] and [Formula: see text]. We describe a set of realizable values [Formula: see text] for arbitrary [Formula: see text], [Formula: see text], and conjecture that this locus is complete. We study the combinatorial structure of the

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26

Shvets, S. V., and V. P. Astakhov. "Effect of Insert Angles on Cutting Tool Geometry." Journal of Engineering Sciences 7, no. 2 (2020): A1—A6. http://dx.doi.org/10.21272/jes.2020.7(2).a1.

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An analysis of publications has shown that mechanically clamped indexable inserts are predominantly used in modern tool manufacturing. Each insert has its shape and geometry in the tool coordinate system. The static system’s required geometry is achieved by the tilting of the insert pocket in the radial and axial directions. Therefore, it is of great importance in the tool design to know the relationships between the insert’s geometry parameters in the tool coordinate system where the geometry paraments of the insert are defined and working geometry parameters of the tool defined in the static

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27

Wang, Wei, Yi Zhang, Gengyu Ge, Huan Yang, and Yue Wang. "A New Approach toward Corner Detection for Use in Point Cloud Registration." Remote Sensing 15, no. 13 (2023): 3375. http://dx.doi.org/10.3390/rs15133375.

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For this study, a new point cloud alignment method is proposed for extracting corner points and aligning them at the geometric level. It can align point clouds that have low overlap and is more robust to outliers and noise. First, planes are extracted from the raw point cloud, and the corner points are defined as the intersection of three planes. Next, graphs are constructed for subsequent point cloud registration by treating corners as vertices and sharing planes as edges. The graph-matching algorithm is then applied to determine correspondence. Finally, point clouds are registered by alignin

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28

Bang, Karl-L., Gunnar Lindberg, and Gandhi Harahap. "Development of Guidelines Based on Life-Cycle Cost To Replace Level-of-Service Concept in Capacity Analysis." Transportation Research Record: Journal of the Transportation Research Board 1572, no. 1 (1997): 10–17. http://dx.doi.org/10.3141/1572-02.

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Highway capacity manuals (HCMs) from developed countries cannot be successfully applied in Indonesia because of significant differences in driver behavior, traffic composition, and level of roadside activities. The Indonesian HCM project (IHCM) was therefore started in 1991 and has resulted in a manual and software for urban traffic facilities, inter-urban roads, and motorways. The IHCM also includes traffic engineering guidelines for selection of appropriate road and intersection type and design for new construction or improvements based on life-cycle cost (LCC) analysis. The LCC model includ

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29

Cayron, Cyril. "The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants." Acta Crystallographica Section A Foundations and Advances 75, no. 3 (2019): 411–37. http://dx.doi.org/10.1107/s205327331900038x.

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The crystallography of displacive/martensitic phase transformations can be described with three types of matrix: the lattice distortion matrix, the orientation relationship matrix and the correspondence matrix. Given here are some formulae to express them in crystallographic, orthonormal and reciprocal bases, and an explanation is offered of how to deduce the matrices of inverse transformation. In the case of the hard-sphere assumption, a continuous form of distortion matrix can be determined, and its derivative is identified to the velocity gradient used in continuum mechanics. The distortion

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30

Patrikalakis, N. M., and P. V. Prakash. "Surface Intersections for Geometric Modeling." Journal of Mechanical Design 112, no. 1 (1990): 100–107. http://dx.doi.org/10.1115/1.2912565.

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Evaluation of planar algebraic curves arises in the context of intersections of algebraic surfaces with piecewise continuous rational polynomial parametric surface patches useful in geometric modeling. We address a method of evaluating these curves of intersection that combines the advantageous features of analytic representation of the governing equation of the algebraic curve in the Bernstein basis within a rectangular domain, adaptive subdivision and polyhedral faceting techniques, and the computation of turning and singular points, to provide the basis for a reliable and efficient solution

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31

Bollobás, Béla, and Alex Scott. "Intersections of graphs." Journal of Graph Theory 66, no. 4 (2011): 261–82. http://dx.doi.org/10.1002/jgt.20489.

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32

Deng, Zhiyun, Yanjun Shi, Qiaomei Han, Lingling Lv, and Weiming Shen. "A Conflict Duration Graph-Based Coordination Method for Connected and Automated Vehicles at Signal-Free Intersections." Applied Sciences 10, no. 18 (2020): 6223. http://dx.doi.org/10.3390/app10186223.

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Previous studies on Connected and Automated Vehicles (CAVs) demonstrated the potential to coordinate the behaviors of multiple connected vehicles for traffic improvements. In this paper, we first propose a Conflict Duration Graph-based (CDG-based) coordination framework to resolve collisions and improve the traffic capacity of signal-free intersections. Secondly, a Speed Control-based Intersection Coordination Model (SICM) is developed to identify complex constraints in multi-vehicle collision scenarios. Thirdly, a geometric Translation-based Intersection Coordination Algorithm (TICA) is propo

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33

Gavril, Fǎnicǎ. "Intersection graphs of proper subtrees of unicyclic graphs." Journal of Graph Theory 18, no. 6 (1994): 615–27. http://dx.doi.org/10.1002/jgt.3190180609.

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34

Chmutov, Sergei, and Sergei Lando. "Mutant knots and intersection graphs." Algebraic & Geometric Topology 7, no. 3 (2007): 1579–98. http://dx.doi.org/10.2140/agt.2007.7.1579.

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35

Cai, Leizhen, Derek Corneil, and Andrzej Proskurowski. "A generalization of line graphs: (X, Y)-intersection graphs." Journal of Graph Theory 21, no. 3 (1996): 267–87. http://dx.doi.org/10.1002/(sici)1097-0118(199603)21:3<267::aid-jgt2>3.0.co;2-o.

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36

Jukna, Stasys. "On set intersection representations of graphs." Journal of Graph Theory 61, no. 1 (2009): 55–75. http://dx.doi.org/10.1002/jgt.20367.

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37

Chen, G., and R. H. Schelp. "Hamiltonian graphs with neighborhood intersections." Journal of Graph Theory 18, no. 5 (1994): 497–513. http://dx.doi.org/10.1002/jgt.3190180508.

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38

Giovanella, A., P. E. Bradley, and S. Wursthorn. "DETECTION AND EVALUATION OF TOPOLOGICAL CONSISTENCY IN CITYGML DATASETS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-4 (September 19, 2018): 59–66. http://dx.doi.org/10.5194/isprs-annals-iv-4-59-2018.

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<p><strong>Abstract.</strong> The topological consistency of Boundary-Representation models, meaning here that the incidence graph is homeomorphic with the underlying topology of geographical data, is checked for several CityGML datasets, and a first classification of topological inconsistencies is performed. The analysis is carried out on a spatial database system into which the datasets have been imported. It is found that real-world datasets contain many topologically inconsistent pairs of intersecting polygons. Also data satisfying the ISO/OGC standards can still be topol

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39

Golubyatnikov, V. P., A. A. Akinshin, N. B. Ayupova, and L. S. Minushkina. "Stratifications and foliations in phase portraits of gene network models." Vavilov Journal of Genetics and Breeding 26, no. 8 (2023): 758–64. http://dx.doi.org/10.18699/vjgb-22-91.

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Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. The variables in these equations describe concentrations of these components as functions of time. In the preparation of numerical experiments with such mathematical models, it is useful to start with studies of qualitative behavior of ense

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40

Eaton, Nancy, and David A. Grable. "Set intersection representations for almost all graphs." Journal of Graph Theory 23, no. 3 (1996): 309–20. http://dx.doi.org/10.1002/(sici)1097-0118(199611)23:3<309::aid-jgt11>3.0.co;2-9.

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41

Tanenbaum, Paul J. "Simultaneous intersection representation of pairs of graphs." Journal of Graph Theory 32, no. 2 (1999): 171–90. http://dx.doi.org/10.1002/(sici)1097-0118(199910)32:2<171::aid-jgt7>3.0.co;2-n.

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42

Pach, János, and Micha Sharir. "On planar intersection graphs with forbidden subgraphs." Journal of Graph Theory 59, no. 3 (2008): 205–14. http://dx.doi.org/10.1002/jgt.20332.

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43

Fachini, Emanuela, and János Körner. "Cross-intersecting couples of graphs." Journal of Graph Theory 56, no. 2 (2007): 105–12. http://dx.doi.org/10.1002/jgt.20252.

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44

Pach, János, Rom Pinchasi, Gábor Tardos, and Géza Tóth. "Geometric graphs with no self-intersecting path of length three." European Journal of Combinatorics 25, no. 6 (2004): 793–811. http://dx.doi.org/10.1016/j.ejc.2003.09.019.

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45

Fys, Mykhailo, Volodymyr Litynskyi, Anatolii Vivat, and Svyatoslav Litynskyi. "GEODESY, CARTOGRAPHY AND AERIAL PHOTOGRAPHY." GEODESY, CARTOGRAPHY AND AERIAL PHOTOGRAPHY 94, 2021, no. 94 (2021): 20–28. http://dx.doi.org/10.23939/istcgcap2021.94.020.

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The aim. The study of formulas determination of the point coordinates by the inverse linear-angular intersection method. Previously, we investigated the possibility of using electronic total stations to control the geometric parameters of industrial buildings. The applied application of electronic total stations for high-precision measurements has been investigated as well. [Vivat, 2018]. The formula for optimal use of the device with certain accuracy characteristics relative to the measured basis is analytically proved and derived [Litynskyi, 2014]. Measurements on the basis of the II categor

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46

Menke, B., T. Zamfirescu, and C. Zamfirescu. "Intersections of longest cycles in grid graphs." Journal of Graph Theory 25, no. 1 (1997): 37–52. http://dx.doi.org/10.1002/(sici)1097-0118(199705)25:1<37::aid-jgt2>3.0.co;2-j.

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47

BOSE, PROSENJIT, HAZEL EVERETT, and STEPHEN WISMATH. "PROPERTIES OF ARRANGEMENT GRAPHS." International Journal of Computational Geometry & Applications 13, no. 06 (2003): 447–62. http://dx.doi.org/10.1142/s0218195903001281.

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An arrangement graph G is the abstract graph obtained from an arrangement of lines L, in general position by associating vertices of G with the intersection points of L, and the edges of G with the line segments joining the intersection points of L. A simple polygon (respectively path) of n sides in general position, induces a set of n lines by extension of the line segments into lines. The main results of this paper are: • Given a graph G, it is NP-Hard to determine if G is the arrangement graph of some set of lines. • There are non-Hamiltonian arrangement graphs for arrangements of six lines

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48

Watanabe, Yohsuke. "Distances and Intersections of Curves." International Mathematics Research Notices 2020, no. 23 (2018): 9674–93. http://dx.doi.org/10.1093/imrn/rny265.

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Abstract We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we study intersection numbers of curves contained in geodesics in the curve graph. Furthermore, we generalize a well-known result on intersection number growth of curves under iteration of Dehn twists and multitwists for all kinds of pure mapping classes.

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49

Paliy, N. "The Use of Descriptive Geometry Methods for Graphical Study of the Parameters of the Cutting Part of a Spiral Drill." Geometry & Graphics 11, no. 2 (2023): 39–46. http://dx.doi.org/10.12737/2308-4898-2023-11-2-39-46.

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The article presents examples of practical application of descriptive geometry methods for solving engineering problems of determining and studying the parameters of the cutting part of a spiral drill. The necessity of graphical constructions is noted, which is due to the fact that it is impossible to measure the rear angle by a direct measurement method using a universal measuring instrument due to the complex geometric shape of the measuring object. The analysis of the geometric shape of the working part of the spiral drill, which includes the main rear conical surface of the drill tooth, th

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50

Petitjean, Sylvain. "A Computational Geometric Approach to Visual Hulls." International Journal of Computational Geometry & Applications 08, no. 04 (1998): 407–36. http://dx.doi.org/10.1142/s0218195998000229.

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Recognizing 3D objects from their 2D silhouettes is a popular topic in computer vision. Object reconstruction can be performed using the volume intersection approach. The visual hull of an object is the best approximation of an object that can be obtained by volume intersection. From the point of view of recognition from silhouettes, the visual hull can not be distinguished from the original object. In this paper, we present efficient algorithms for computing visual hulls. We start with the case of planar figures (polygons and curved objects) and base our approach on an efficient algorithm for

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