An Efficient Heuristic Algorithm for Solving Connected Vertex Cover Problem

Zhang, Yongfei; Wu, Jun; Zhang, Liming; Zhao, Peng; Zhou, Junping; Yin, Minghao

doi:10.1155/2018/3935804

Cited by 4 publications

(4 citation statements)

References 24 publications

(40 reference statements)

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“…In this way, the heuristic algorithm is always directed to the best choice, but at a local level. However, this choice may prove inappropriate at the global level [39][40][41][42]. Heuristic algorithms are not difficult to create, respectively, and their implementation is not complicated.…”

Section: Literature Reviewmentioning

confidence: 99%

An Interactive Application for Learning and Analyzing Different Graph Vertex Cover Algorithms

2023

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This paper deals with an analysis of three algorithms for the graph vertex cover problem. Certain methods for solving this problem are analyzed. In addition, different studies on the problem and some approaches to its solution are discussed as well. An exact algorithm (based on the backtracking approach) is presented. Calculating the average time for execution of this algorithm is consistent with the multitasking way of work of the operating system. For this purpose, four different starts of the algorithm are made and then the average time of all of them is calculated. The exact algorithm found the optimal solutions for all analyzed graphs. Besides this algorithm, two other heuristic algorithms for solving the problem are discussed. For this study, an interactive application is developed to visualize the performance of the three algorithms and display the obtained results. The results show that for small graphs with no more than 25 vertices the exact algorithm can be used to solve optimally the graph vertex cover problem. For the largest graphs, none of the two heuristic algorithms found the optimal solutions, but these algorithms generated solutions that are very close to the optimal ones. In summary, when the size of the graph increases linearly, the execution time of the heuristic algorithms increases linearly, while the execution time of the exact algorithm increases exponentially.

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Section: Literature Reviewmentioning

confidence: 99%

An Interactive Application for Learning and Analyzing Different Graph Vertex Cover Algorithms

2023

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“…They have planned this parameter for a number of classes of graphs. Zhang et al (2018) offered a well-organized algorithm GRASP-CVC (Greedy Randomized Adaptive Search Procedure for Connected Vertex Cover) for CVC in general graphs. Kuhn et al (2013) examined the weighted vertex cover problem in graphs when a nearby bounded coloring is given.…”

Section: Graph Coloring Problemmentioning

confidence: 99%

Suitable Site Selection of Water ATMs (Basis of Interior/Exterior Conditions) Using Graph Theory

Ahmed

Islam

Bora

2022

Journal of Cases on Information Technology

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Maintenance performs a vital role in assuring safety operation, enhancing the quality and accumulating the durability of the system. In this paper a method has been evolved to solve the different kinds of issues like new software installation, upgradation of current software, fixing of required equipment, raw water supply problem etc. To continue the service of water ATMs we cannot start maintenance of all the water ATMs together in any particular site, so authors require a proper network planning. Authors have a developed an algorithm to select the best site for fixing of Water ATMs. So individual can use this algorithm and find out the best sites for setting up of Water ATMs such that maximum numbers of persons gain the advantage of Water ATMs. In addition authors have planned an IoT enable Water ATMs. The IoT enabled technology put in the various function of Water ATMs, safeguarding the quality of water.

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“…Johnson et al concerned the CVC problem for some special cases of graphs [45]. A two stage algorithm has been given in [46] where a greedy algorithm is used in construction stage and a configuration checking method is used in local search stage. In [47], CVC problem on k-regular problems for constant k values where k ≥ 4 is studied.…”

Section: Related Workmentioning

confidence: 99%

Weighted Connected Vertex Cover Based Energy-Efficient Link Monitoring for Wireless Sensor Networks Towards Secure Internet of Things

Dagdeviren

2021

IEEE Access

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Industry 4.0 utilizes the Internet of Things (IoT) to rise the efficiency in manufacturing and automation where wireless sensor networks (WSNs) are crucial technologies for communication layer of IoT. WSNs include hundreds of small sized sensor nodes that have the abilities of wireless transmission and environmental sensing. Wireless transmission is prone to various attacks such as data manipulation since data communication is achieved through transfer of radio packets. A countermeasure of this issue is link monitoring by deploying secure points that can physically capture and inspect radio packets. Graph theory plays a critical role to solve various problems in WSNs. Finding minimum Vertex Cover (VC) is an important NP-Hard graph theoretic problem in which the minimum set of nodes (vertices) is aimed to select in such a way that each link should be incident to at least one node from this set. VC is a significant structure for WSNs where it perfectly fits for link monitoring when nodes in VC are set as secure points (monitors). Since sensor nodes are generally battery-powered and have limited transmission range, energy-efficient multi-hop communication to the sink node is of utmost importance. In weighted connected VC (WCVC) structure, subgraph induced by monitor nodes are connected where monitors are chosen according to their weights. When weights of nodes are assigned as reciprocal of their energies, an energy-efficient virtual backbone can be formed. We propose a novel metaheuristic WCVC algorithm for link monitoring and backbone formation in WSNs modeled as undirected graphs. Our proposed algorithm integrates a genetic search with a greedy heuristic to improve WCVC solution quality and decrease the search time. To evaluate the efficiencies of greedy heuristics, we adopt three different heuristics for WCVC problem. We implement our algorithm with its counterparts and reveal that the algorithm is favorable in terms of solution quality and resource consumption. INDEX TERMS Internet of things, wireless sensor networks, link monitoring, vertex cover, metaheuristic algorithm.

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An Efficient Heuristic Algorithm for Solving Connected Vertex Cover Problem

Cited by 4 publications

References 24 publications

An Interactive Application for Learning and Analyzing Different Graph Vertex Cover Algorithms

An Interactive Application for Learning and Analyzing Different Graph Vertex Cover Algorithms

Suitable Site Selection of Water ATMs (Basis of Interior/Exterior Conditions) Using Graph Theory

Weighted Connected Vertex Cover Based Energy-Efficient Link Monitoring for Wireless Sensor Networks Towards Secure Internet of Things

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