Weighted Maximum-Clique Transversal Sets of Graphs

Lee, Chuan-Min

doi:10.5402/2011/540834

Cited by 4 publications

(2 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See the recent work of Shan et al [52] and references therein. In computer science, exactly computing the smallest set on special classes of graphs appears in many works [35,46,13,27,47].…”

Section: Cliquesmentioning

confidence: 99%

Inapproximability of $H$-Transversal/Packing

Guruswami

Lee

2017

SIAM J. Discrete Math.

View full text Add to dashboard Cite

Given an undirected graph G = (V G , E G ) and a fixed "pattern" graph H = (V H , E H ) with k vertices, we consider the H-Transversal and H-Packing problems. The former asks to find the smallest S ⊆ V G such that the subgraph induced by V G \ S does not have H as a subgraph, and the latter asks to find the maximum number of pairwise disjoint k-subsets S 1 , ..., S m ⊆ V G such that the subgraph induced by each S i has H as a subgraph.We prove that if H is 2-connected, H-Transversal and H-Packing are almost as hard to approximate as general k-Hypergraph Vertex Cover and k-Set Packing, so it is NP-hard to approximate them within a factor of Ω(k) and Ω(k) respectively. We also show that there is a 1-connected H where H-Transversal admits an O(log k)-approximation algorithm, so that the connectivity requirement cannot be relaxed from 2 to 1. For a special case of H-Transversal where H is a (family of) cycles, we mention the implication of our result to the related Feedback Vertex Set problem, and give a different hardness proof for directed graphs. * It is an expanded, generalized, and refocused version of our earlier unpublished manuscript [33] and our conference version that appears in the proceedings of APPROX 15. †

show abstract

“…See the recent work of Shan et al [52] and references therein. In computer science, exactly computing the smallest set on special classes of graphs appears in many works [35,46,13,27,47].…”

Section: Cliquesmentioning

confidence: 99%

Inapproximability of $H$-Transversal/Packing

Guruswami

Lee

2017

SIAM J. Discrete Math.

View full text Add to dashboard Cite

show abstract

“…The clique transversal problem (CTP) and its variants have received significant attention in the past two decades due to their theoretical importance and practical applications in various fields such as communication networks [1][2][3][4][5][6][7], social-network theory [8][9][10][11][12] and cellular-telephone transceiver placement [13][14][15][16][17][18][19]. Most of the research in this area revolves around two fundamental computational complexity classes: P and NP.…”

Section: Introductionmentioning

confidence: 99%

Clique Transversal Variants on Graphs: A Parameterized-Complexity Perspective

Lee

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

The clique transversal problem and its variants have garnered significant attention in the last two decades due to their practical applications in communication networks, social-network theory and transceiver placement for cellular telephones. While previous research primarily focused on determining the polynomial-time solvability or NP-hardness/NP-completeness of specific graphs, this paper adopts a parameterized-complexity approach. It thoroughly explores four clique transversal variants: the d-fold transversal problem, the {d}-clique transversal problem, the signed clique transversal problem and the minus clique transversal problem. The paper presents various findings regarding the parameterized complexity of the clique transversal problem and its variants. It establishes the W[2]-completeness and para-NP-completeness of the d-fold transversal problem, the {d}-clique transversal problem, the signed clique transversal problem and the minus clique transversal problem within specific graph classes. Additionally, it introduces fixed-parameter tractable algorithms for planar graphs and graphs with bounded treewidth, offering efficient solutions for these specific instances of the problems. The research further explores the relationship between planar graphs and graphs with bounded treewidth to enhance the time complexity of the d-fold clique transversal problem and the {d}-clique transversal problem. By analyzing the parameterized complexity of the clique transversal problem and its variants, this research contributes to our understanding of the computational limitations and potentially efficient algorithms for solving these problems.

show abstract