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Journal articles on the topic 'Connected vertex cover problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Zhang, Yongfei, Jun Wu, Liming Zhang, Peng Zhao, Junping Zhou, and Minghao Yin. "An Efficient Heuristic Algorithm for Solving Connected Vertex Cover Problem." Mathematical Problems in Engineering 2018 (September 6, 2018): 1–10. http://dx.doi.org/10.1155/2018/3935804.

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The connected vertex cover (CVC) problem, which has many important applications, is a variant of the vertex cover problem, such as wireless network design, routing, and wavelength assignment problem. A good algorithm for the problem can help us improve engineering efficiency, cost savings, and resources consumption in industrial applications. In this work, we present an efficient algorithm GRASP-CVC (Greedy Randomized Adaptive Search Procedure for Connected Vertex Cover) for CVC in general graphs. The algorithm has two main phases, i.e., construction phase and local search phase. In the constr

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2

Li, Yuchao, Wei Wang, and Zishen Yang. "The connected vertex cover problem in k-regular graphs." Journal of Combinatorial Optimization 38, no. 2 (2019): 635–45. http://dx.doi.org/10.1007/s10878-019-00403-3.

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3

Li, Yuchao, Zishen Yang, and Wei Wang. "Complexity and algorithms for the connected vertex cover problem in 4-regular graphs." Applied Mathematics and Computation 301 (May 2017): 107–14. http://dx.doi.org/10.1016/j.amc.2016.12.004.

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4

Liu, Xianliang, Hongliang Lu, Wei Wang, and Weili Wu. "PTAS for the minimum k-path connected vertex cover problem in unit disk graphs." Journal of Global Optimization 56, no. 2 (2011): 449–58. http://dx.doi.org/10.1007/s10898-011-9831-x.

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5

Escoffier, Bruno, Laurent Gourvès, and Jérôme Monnot. "Complexity and approximation results for the connected vertex cover problem in graphs and hypergraphs." Journal of Discrete Algorithms 8, no. 1 (2010): 36–49. http://dx.doi.org/10.1016/j.jda.2009.01.005.

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6

Rana, Akul, Anita Pal, and Madhumangal Pal. "An Efficient Algorithm to Solve the Conditional Covering Problem on Trapezoid Graphs." ISRN Discrete Mathematics 2011 (November 17, 2011): 1–10. http://dx.doi.org/10.5402/2011/213084.

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Let G=(V,E) be a simple connected undirected graph. Each vertex v∈V has a cost c(v) and provides a positive coverage radius R(v). A distance duv is associated with each edge {u,v}∈E, and d(u,v) is the shortest distance between every pair of vertices u,v∈V. A vertex v can cover all vertices that lie within the distance R(v), except the vertex itself. The conditional covering problem is to minimize the sum of the costs required to cover all the vertices in G. This problem is NP-complete for general graphs, even it remains NP-complete for chordal graphs. In this paper, an O(n2) time algorithm to

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7

Wang, Limin, Xiaoyan Zhang, Zhao Zhang, and Hajo Broersma. "A PTAS for the minimum weight connected vertex cover P3 problem on unit disk graphs." Theoretical Computer Science 571 (March 2015): 58–66. http://dx.doi.org/10.1016/j.tcs.2015.01.005.

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8

Fan, Lidan, Zhao Zhang, and Wei Wang. "PTAS for minimum weighted connected vertex cover problem with c-local condition in unit disk graphs." Journal of Combinatorial Optimization 22, no. 4 (2010): 663–73. http://dx.doi.org/10.1007/s10878-010-9315-9.

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9

DINITZ, YEFIM, MATTHEW J. KATZ, and ROI KRAKOVSKI. "GUARDING RECTANGULAR PARTITIONS." International Journal of Computational Geometry & Applications 19, no. 06 (2009): 579–94. http://dx.doi.org/10.1142/s0218195909003131.

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A rectangular partition is a partition of a rectangle into non-overlapping rectangles, such that no four rectangles meet at a common point. A vertex guard is a guard located at a vertex of the partition (i.e., at a corner of a rectangle); it guards the rectangles that meet at this vertex. An edge guard is a guard that patrols along an edge of the partition, and is thus equivalent to two adjacent vertex guards. We consider the problem of finding a minimum-cardinality guarding set for the rectangles of the partition. For vertex guards, we prove that guarding a given subset of the rectangles is N

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10

Wang, Limin, Wenxue Du, Zhao Zhang, and Xiaoyan Zhang. "A PTAS for minimum weighted connected vertex cover $$P_3$$ P 3 problem in 3-dimensional wireless sensor networks." Journal of Combinatorial Optimization 33, no. 1 (2015): 106–22. http://dx.doi.org/10.1007/s10878-015-9937-z.

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11

Wang, Shiping, Qingxin Zhu, William Zhu, and Fan Min. "Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/519173.

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Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, corresponding problems in graphs are also transformed into ones in covering-based rough sets. For example, finding a minimal edge cover of a graph is translated into finding a minimal general reduct of a covering.

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12

Balister, Paul, Béla Bollobás, Amites Sarkar, and Mark Walters. "Connectivity of random k-nearest-neighbour graphs." Advances in Applied Probability 37, no. 01 (2005): 1–24. http://dx.doi.org/10.1017/s000186780000001x.

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Let 𝓅 be a Poisson process of intensity one in a square S n of area n. We construct a random geometric graph G n,k by joining each point of 𝓅 to its k ≡ k(n) nearest neighbours. Recently, Xue and Kumar proved that if k ≤ 0.074 log n then the probability that G n, k is connected tends to 0 as n → ∞ while, if k ≥ 5.1774 log n, then the probability that G n, k is connected tends to 1 as n → ∞. They conjectured that the threshold for connectivity is k = (1 + o(1)) log n. In this paper we improve these lower and upper bounds to 0.3043 log n and 0.5139 log n, respectively, disproving this conjecture

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13

Balister, Paul, Béla Bollobás, Amites Sarkar, and Mark Walters. "Connectivity of random k-nearest-neighbour graphs." Advances in Applied Probability 37, no. 1 (2005): 1–24. http://dx.doi.org/10.1239/aap/1113402397.

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Let 𝓅 be a Poisson process of intensity one in a square Sn of area n. We construct a random geometric graph Gn,k by joining each point of 𝓅 to its k ≡ k(n) nearest neighbours. Recently, Xue and Kumar proved that if k ≤ 0.074 log n then the probability that Gn, k is connected tends to 0 as n → ∞ while, if k ≥ 5.1774 log n, then the probability that Gn, k is connected tends to 1 as n → ∞. They conjectured that the threshold for connectivity is k = (1 + o(1)) log n. In this paper we improve these lower and upper bounds to 0.3043 log n and 0.5139 log n, respectively, disproving this conjecture. We

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14

González Yero, Ismael. "The Simultaneous Strong Resolving Graph and the Simultaneous Strong Metric Dimension of Graph Families." Mathematics 8, no. 1 (2020): 125. http://dx.doi.org/10.3390/math8010125.

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We consider in this work a new approach to study the simultaneous strong metric dimension of graphs families, while introducing the simultaneous version of the strong resolving graph. In concordance, we consider here connected graphs G whose vertex sets are represented as V ( G ) , and the following terminology. Two vertices u , v ∈ V ( G ) are strongly resolved by a vertex w ∈ V ( G ) , if there is a shortest w − v path containing u or a shortest w − u containing v. A set A of vertices of the graph G is said to be a strong metric generator for G if every two vertices of G are strongly resolve

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15

Petrenjuk, V. I., and D. A. Petrenjuk. "About Structure of Graph Obstructions for Klein Surface with 9 Vertices." Cybernetics and Computer Technologies, no. 4 (December 31, 2020): 65–86. http://dx.doi.org/10.34229/2707-451x.20.4.5.

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The structure of the 9 vertex obstructive graphs for the nonorientable surface of the genus 2 is established by the method of j-transformations of the graphs. The problem of establishing the structural properties of 9 vertex obstruction graphs for the surface of the undirected genus 2 by the method of j-transformation of graphs is considered. The article has an introduction and 5 sections. The introduction contains the main definitions, which are illustrated, to some extent, in Section 1, which provides several statements about their properties. Sections 2 – 4 investigate the structural proper

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16

Hassin, Refael, and Asaf Levin. "The minimum generalized vertex cover problem." ACM Transactions on Algorithms 2, no. 1 (2006): 66–78. http://dx.doi.org/10.1145/1125994.1125998.

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17

Johnson, Matthew, Giacomo Paesani, and Daniël Paulusma. "Connected Vertex Cover for $$(sP_1+P_5)$$-Free Graphs." Algorithmica 82, no. 1 (2019): 20–40. http://dx.doi.org/10.1007/s00453-019-00601-9.

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18

Majumdar, Diptapriyo, M. S. Ramanujan, and Saket Saurabh. "On the Approximate Compressibility of Connected Vertex Cover." Algorithmica 82, no. 10 (2020): 2902–26. http://dx.doi.org/10.1007/s00453-020-00708-4.

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19

Ma, Changcun, Donghyun Kim, Yuexuan Wang, Wei Wang, Nassim Sohaee, and Weili Wu. "Hardness of k-Vertex-Connected Subgraph Augmentation Problem." Journal of Combinatorial Optimization 20, no. 3 (2009): 249–58. http://dx.doi.org/10.1007/s10878-008-9206-5.

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20

Zhang, Zhao, Xiaofeng Gao, and Weili Wu. "Algorithms for connected set cover problem and fault-tolerant connected set cover problem." Theoretical Computer Science 410, no. 8-10 (2009): 812–17. http://dx.doi.org/10.1016/j.tcs.2008.11.005.

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21

Hartmann, Alexander K., and Martin Weigt. "Statistical mechanics of the vertex-cover problem." Journal of Physics A: Mathematical and General 36, no. 43 (2003): 11069–93. http://dx.doi.org/10.1088/0305-4470/36/43/028.

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22

Boria, Nicolas, Federico Della Croce, and Vangelis Th Paschos. "On the max min vertex cover problem." Discrete Applied Mathematics 196 (December 2015): 62–71. http://dx.doi.org/10.1016/j.dam.2014.06.001.

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23

Tu, Jianhua, and Fengmei Yang. "The vertex cover problem in cubic graphs." Information Processing Letters 113, no. 13 (2013): 481–85. http://dx.doi.org/10.1016/j.ipl.2013.04.002.

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24

Krithika, R., Diptapriyo Majumdar, and Venkatesh Raman. "Revisiting Connected Vertex Cover: FPT Algorithms and Lossy Kernels." Theory of Computing Systems 62, no. 8 (2018): 1690–714. http://dx.doi.org/10.1007/s00224-017-9837-y.

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25

Zhang, Zhao, Xiaofeng Gao, and Weili Wu. "PTAS for connected vertex cover in unit disk graphs." Theoretical Computer Science 410, no. 52 (2009): 5398–402. http://dx.doi.org/10.1016/j.tcs.2009.01.035.

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26

Liu, Pengcheng, Zhao Zhang, Xianyue Li, and Weili Wu. "Approximation algorithm for minimum connected 3-path vertex cover." Discrete Applied Mathematics 287 (December 2020): 77–84. http://dx.doi.org/10.1016/j.dam.2020.08.008.

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27

DA SILVA, MARIANA O., GUSTAVO A. GIMENEZ-LUGO, and MURILO V. G. DA SILVA. "VERTEX COVER IN COMPLEX NETWORKS." International Journal of Modern Physics C 24, no. 11 (2013): 1350078. http://dx.doi.org/10.1142/s0129183113500782.

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A Minimum Vertex Cover is the smallest set of vertices whose removal completely disconnects a graph. In this paper, we perform experiments on a number of graphs from standard complex networks databases addressing the problem of finding a "good" vertex cover (finding an optimum is a NP-Hard problem). In particular, we take advantage of the ubiquitous power law distribution present on many complex networks. In our experiments, we show that running a greedy algorithm in a power law graph we can obtain a very small vertex cover typically about 1.02 times the theoretical optimum. This is an interes

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28

Mölle, Daniel, Stefan Richter, and Peter Rossmanith. "Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover." Theory of Computing Systems 43, no. 2 (2007): 234–53. http://dx.doi.org/10.1007/s00224-007-9089-3.

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29

Fujito, Toshihiro, and Takashi Doi. "A 2-approximation NC algorithm for connected vertex cover and tree cover." Information Processing Letters 90, no. 2 (2004): 59–63. http://dx.doi.org/10.1016/j.ipl.2004.01.011.

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30

Younis, Althoby Haeder. "An efficient algorithm for st-Connected Vertex Separator problem." Journal of Physics: Conference Series 1999, no. 1 (2021): 012113. http://dx.doi.org/10.1088/1742-6596/1999/1/012113.

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31

Roy, Sharadindu, Prof Samer Sen Sarma, Soumyadip Chakravorty, and Suvodip Maity. "A COMPARATIVE STUDY OF VARIOUS METHODS OF ANN FOR SOLVING TSP PROBLEM." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 4, no. 1 (2013): 19–28. http://dx.doi.org/10.24297/ijct.v4i1a.3029.

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Abstract This paper represents TSP (Travelling Salesman Problem) by using Artificial Neural Networks.A comparative study of various methods of ANN is shown here for solving TSP problem.The Travelling Salesman Problem is a classical combinational optimization problem, which is a simple to state but very difficult to solve. This problem is to find the shortest possible tour through a set of N vertices so that each vertex is visited exactly once. TSP can be solved by Hopfield Network, Self-organization Map, and Simultaneous Recurrent Network. Hopfield net is a fully connected network, where every

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32

SINGH, ALOK, and ASHOK KUMAR GUPTA. "A HYBRID HEURISTIC FOR THE MINIMUM WEIGHT VERTEX COVER PROBLEM." Asia-Pacific Journal of Operational Research 23, no. 02 (2006): 273–85. http://dx.doi.org/10.1142/s0217595906000905.

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Given an undirected graph with weights associated with its vertices, the minimum weight vertex cover problem seeks a subset of vertices with minimum sum of weights such that each edge of the graph has at least one endpoint belonging to the subset. In this paper, we propose a hybrid approach, combining a steady-state genetic algorithm and a greedy heuristic, for the minimum weight vertex cover problem. The genetic algorithm generates vertex cover, which is then reduced to minimal weight vertex cover by the heuristic. We have evaluated the performance of our algorithm on several test problems of

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33

Kowalik, Łukasz, Marcin Pilipczuk, and Karol Suchan. "Towards optimal kernel for connected vertex cover in planar graphs." Discrete Applied Mathematics 161, no. 7-8 (2013): 1154–61. http://dx.doi.org/10.1016/j.dam.2012.12.001.

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34

Li, Xiaosong, Zhao Zhang, and Xiaohui Huang. "Approximation algorithms for minimum (weight) connected k-path vertex cover." Discrete Applied Mathematics 205 (May 2016): 101–8. http://dx.doi.org/10.1016/j.dam.2015.12.004.

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35

Ran, Yingli, Zhao Zhang, Xiaohui Huang, Xiaosong Li, and Ding-Zhu Du. "Approximation algorithms for minimum weight connected 3-path vertex cover." Applied Mathematics and Computation 347 (April 2019): 723–33. http://dx.doi.org/10.1016/j.amc.2018.11.045.

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36

Kettani, Omar, Faycal Ramdani, and Benaissa Tadili. "A Heuristic Approach for the Vertex Cover Problem." International Journal of Computer Applications 82, no. 4 (2013): 9–11. http://dx.doi.org/10.5120/14102-2126.

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37

Wang, Luzhi, Shuli Hu, Mingyang Li, and Junping Zhou. "An Exact Algorithm for Minimum Vertex Cover Problem." Mathematics 7, no. 7 (2019): 603. http://dx.doi.org/10.3390/math7070603.

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In this paper, we propose a branch-and-bound algorithm to solve exactly the minimum vertex cover (MVC) problem. Since a tight lower bound for MVC has a significant influence on the efficiency of a branch-and-bound algorithm, we define two novel lower bounds to help prune the search space. One is based on the degree of vertices, and the other is based on MaxSAT reasoning. The experiment confirms that our algorithm is faster than previous exact algorithms and can find better results than heuristic algorithms.

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38

Wang, Rong Long, Zheng Tang, and Xin Shun Xu. "An Efficient Algorithm for Minimum Vertex Cover Problem." IEEJ Transactions on Electronics, Information and Systems 124, no. 7 (2004): 1494–99. http://dx.doi.org/10.1541/ieejeiss.124.1494.

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39

Hasudungan, Rofilde, Dwi M. Pangestuty, Asslia J. Latifah, and Rudiman. "Solving Minimum Vertex Cover Problem Using DNA Computing." Journal of Physics: Conference Series 1361 (November 2019): 012038. http://dx.doi.org/10.1088/1742-6596/1361/1/012038.

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40

Bera, Suman K., Shalmoli Gupta, Amit Kumar, and Sambuddha Roy. "Approximation algorithms for the partition vertex cover problem." Theoretical Computer Science 555 (October 2014): 2–8. http://dx.doi.org/10.1016/j.tcs.2014.04.006.

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41

Brešar, B., R. Krivoš-Belluš, G. Semanišin, and P. Šparl. "On the weighted k-path vertex cover problem." Discrete Applied Mathematics 177 (November 2014): 14–18. http://dx.doi.org/10.1016/j.dam.2014.05.042.

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42

Bertolazzi, Paola, and Antonio Sassano. "A decomposition strategy for the vertex cover problem." Information Processing Letters 31, no. 6 (1989): 299–304. http://dx.doi.org/10.1016/0020-0190(89)90091-4.

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43

Pandey, Pooja, and Abraham P. Punnen. "The generalized vertex cover problem and some variations." Discrete Optimization 30 (November 2018): 121–43. http://dx.doi.org/10.1016/j.disopt.2018.06.004.

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44

Brause, Christoph, and Ingo Schiermeyer. "Kernelization of the 3-path vertex cover problem." Discrete Mathematics 339, no. 7 (2016): 1935–39. http://dx.doi.org/10.1016/j.disc.2015.12.006.

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45

Li, Ruizhi, Shuli Hu, Huan Liu, Ruiting Li, Dantong Ouyang, and Minghao Yin. "Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems." Mathematics 7, no. 12 (2019): 1173. http://dx.doi.org/10.3390/math7121173.

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The minimum connected dominating set (MCDS) problem is a very significant NP-hard combinatorial optimization problem, and it has been used in many fields such as wireless sensor networks and ad hoc networks. In this paper, we propose a novel multi-start local search algorithm (MSLS) to tackle the minimum connected dominating set problem. Firstly, we present the fitness mechanism to design the vertex score mechanism so that our algorithm can jump out of the local optimum. Secondly, we use the configuration checking (CC) mechanism to avoid the cycling problem. Then, we propose the vertex flippin

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46

Sheng, Cheng, Yufei Tao, and Jianzhong Li. "Exact and approximate algorithms for the most connected vertex problem." ACM Transactions on Database Systems 37, no. 2 (2012): 1–39. http://dx.doi.org/10.1145/2188349.2188354.

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47

Ren, Wei, and Qing Zhao. "A note on ‘Algorithms for connected set cover problem and fault-tolerant connected set cover problem’." Theoretical Computer Science 412, no. 45 (2011): 6451–54. http://dx.doi.org/10.1016/j.tcs.2011.07.008.

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48

Pushpam, P. Roushini Leely, and Chitra Suseendran. "Secure vertex cover of a graph." Discrete Mathematics, Algorithms and Applications 09, no. 02 (2017): 1750026. http://dx.doi.org/10.1142/s1793830917500264.

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We study the problem of using mobile guards to defend the vertices of a graph [Formula: see text] against a single attack on its vertices. A vertex cover of a graph [Formula: see text] is a set [Formula: see text] such that for each edge [Formula: see text], at least one of [Formula: see text] or [Formula: see text] is in [Formula: see text]. The minimum cardinality of a vertex cover is termed the vertex covering number and it is denoted by [Formula: see text]. In this context, we introduce a new protection strategy called the secure vertex cover[Formula: see text]SVC[Formula: see text] proble

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49

Han, Keun-Hee, and Chan-Soo Kim. "Applying Genetic Algorithm to the Minimum Vertex Cover Problem." KIPS Transactions:PartB 15B, no. 6 (2008): 609–12. http://dx.doi.org/10.3745/kipstb.2008.15-b.6.609.

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50

Karakostas, George. "A better approximation ratio for the vertex cover problem." ACM Transactions on Algorithms 5, no. 4 (2009): 1–8. http://dx.doi.org/10.1145/1597036.1597045.

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