Approximation algorithms for minimum weight connected 3-path vertex cover

Ran, Yingli; Zhang, Zhao; Huang, Xiaohui; Li, Xiaosong; Du, Ding‐Zhu

doi:10.1016/j.amc.2018.11.045

Cited by 10 publications

(6 citation statements)

References 24 publications

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“…For WC-MinVCP 3 , Ran et al [56] presented a (ln ∆ + 4 + ln 2)-approximation algorithm, where ∆ is the maximum degree of the input graph. Wang et al [72] showed that the problem remains NP-hard when restricted to unit disk graphs and gave a PTAS for the problem on unit disk graphs under the assumption that the problem is c-local and the unit disk graphs have minimum degree of at least two.…”

Section: Theorem 42 [45]mentioning

confidence: 99%

A Survey on the k-Path Vertex Cover Problem

Tu¹

2022

Preprint

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Given a graph G = (V, E) and a positive integer k ≥ 2, a k-path vertex cover is a subset of vertices F such that every path on k vertices in G contains at least one vertex from F . A minimum k-path vertex cover in G is a k-path vertex cover with minimum cardinality and its cardinality is called the k-path vertex cover number of G. In the k-path vertex cover problem, it is required to find a minimum k-path vertex cover in a given graph. In this paper, we present a brief survey of the current state of the art in the study of the k-path vertex cover problem and the k-path vertex cover number.

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Section: Theorem 42 [45]mentioning

confidence: 99%

A Survey on the k-Path Vertex Cover Problem

Tu¹

2022

Preprint

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“…Hence we study UG which is more realistic model in this manner. We also left WCVC studies having different constraints (such as every path consisting of k vertices has one monitor node) [49], [50] that are out of our scope.…”

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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“…Subsequent work regarding the maximum variant [7] and weighted variant [3] of k-Path Vertex Cover has also been considered in the literature. Recently, the study of k-Path Vertex Cover and related problems has gained a lot of attraction from both theoretical aspect [10,11] and practical application [5].…”

Section: Introductionmentioning

confidence: 99%

TS-Reconfiguration of $k$-Path Vertex Covers in Caterpillars for $k \geq 4$

Hoang¹

2022

Preprint

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A k-path vertex cover (k-PVC) of a graph G is a vertex subset I such that each path on k vertices in G contains at least one member of I. Imagine that a token is placed on each vertex of a k-PVC. Given two k-PVCs I, J of a graph G, the k-Path Vertex Cover Reconfiguration (k-PVCR) under Token Sliding (TS) problem asks if there is a sequence of k-PVCs between I and J where each intermediate member is obtained from its predecessor by sliding a token from some vertex to one of its unoccupied neighbors. This problem is known to be PSPACE-complete even for planar graphs of maximum degree 3 and bounded treewidth and can be solved in polynomial time for paths and cycles. Its complexity for trees remains unknown. In this paper, for k ≥ 4, we present a polynomial-time algorithm that solves k-PVCR under TS for caterpillars (i.e., trees formed by attaching leaves to a path).

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Approximation algorithms for minimum weight connected 3-path vertex cover

Cited by 10 publications

References 24 publications

A Survey on the k-Path Vertex Cover Problem

A Survey on the k-Path Vertex Cover Problem

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

TS-Reconfiguration of $k$-Path Vertex Covers in Caterpillars for $k \geq 4$

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