A factor 2 approximation algorithm for the vertex cover problem

Tu, Jianhua; Zhou, Wenli

doi:10.1016/j.ipl.2011.04.009

Cited by 67 publications

(30 citation statements)

References 8 publications

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“…if G consists of two intersecting maximal cliques C 1 and C 2 then return the smaller of C 1 ∩ C 2 , C 1 \ C 2 , and C 1 \ C 2 ; 5. find all maximal strong modules of G and build Q(G); 6. if a maximal strong module M is not a clique then return APPROX-ASSO(G − N G [M])∪N G (M); 7. define a weighted graph Q, and call the algorithm of [20] with it;…”

Section: The Approximation Algorithmmentioning

confidence: 99%

Approximate Association via Dissociation

Jie

Wang

Cao

2016

Graph-Theoretic Concepts in Computer Science

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A vertex set X of a graph G is an association set if each component of G − X is a clique, or a dissociation set if each component of G − X is a single vertex or a single edge. Interestingly, G − X is then precisely a graph containing no induced P 3 's or containing no P 3 's, respectively. We observe some special structures and show that if none of them exists, then the minimum association set problem can be reduced to the minimum (weighted) dissociation set problem. This yields the first nontrivial approximation algorithm for association set, and its approximation ratio is 2.5, matching the best result of the closely related cluster editing problem. The reduction is based on a combinatorial study of modular decomposition of graphs free of these special structures. Further, a novel algorithmic use of modular decomposition enables us to implement this approach in O(mn + n 2 ) time.

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Section: The Approximation Algorithmmentioning

confidence: 99%

Approximate Association via Dissociation

Jie

Wang

Cao

2016

Graph-Theoretic Concepts in Computer Science

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“…Tu and Zhou in [19] considered the vertex weighted version of the VCP k motivated by its applications in traffic control along with the aforementioned. In general, VCP k is known to be NP-complete, for k ≥ 2, [5,19]. Brešar et al [5] present a linear time algorithm for trees and investigate upper bounds on ψ k (G) in regular graphs.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, VCP 3 is APX-complete and Fujito's local ratio based algorithm [8] approximates VCP 3 within a factor of 2. In [19], the authors presented a primal-dual factor 2 approximation algorithm for VCP 3 , which is based on a new integer linear program formulation. Tu and Yang [18] give a 1.57-approximation to VCP 3 in cubic graphs.…”

Section: Introductionmentioning

confidence: 99%

“…The approximability of the generalized problem of the two above mentioned node deletion problems in the direction of bounding the degree has been studied extensively in [6][7][8]16]. The method of formulating VCP 3 as an integer linear program formulation as in [19] does not get extended to have an integer linear program formulation for VCP k , for k > 3. Based on the lower bound results for Min-BDD-b [16], we expect that VCP k may not be approximable within a constant factor for arbitrary k. We define VCP 4 as: Given a graph G = (V , E), find a set S ⊆ V of minimum size such that G[V \ S] contains no path on 4 vertices.…”

Section: Introductionmentioning

confidence: 99%

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Computational complexity of minimum P4 vertex cover problem for regular and K1,4
Devi
¹
,
Mane
²
,
Mishra
³

2015
Discrete Applied Mathematics
14
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2
0
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a b s t r a c tIn VCP 4 problem, it is asked to find a set S ⊆ V of minimum size such that G[V \ S] contains no path on 4 vertices, in a given graph G = (V , E). We prove that it is APX-complete for 3-regular graphs as well as 3-regular bipartite graphs. We show that a greedy based algorithm approximates VCP 4 within a factor of 2 for regular graphs. We also show that VCP 4 is APX-complete for K 1,4 -free graphs and a local ratio based algorithm generates a solution which is within a factor of 3.

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“…k-Path Transversal is motivated by applications in transportation / wireless sensor networks, and has also been actively studied as k-Path Vertex Cover or P k -Hitting Set [32,7,6,9,21] in terms of their approximability and fixed parameter tractability. Tu and Zhou [32] gave a 2-approximation algorithm for 3-Path Transversal. Camby [9] recently gave a 3-approximation algorithm for 4-Path Transversal.…”

mentioning

confidence: 99%