On approximating minimum vertex cover for graphs with perfect matching

被引：5
|
作者：
Chen, JN
Kanj, IA
机构：
[1] Depaul Univ, Sch CTI, Chicago, IL 60604 USA
[2] Texas A&M Univ, Dept Comp Sci, College Stn, TX 77843 USA
[3] Cent S Univ, Coll Informat Sci & Engn, Changsha 410083, Peoples R China
来源：
THEORETICAL COMPUTER SCIENCE | 2005年 / 337卷 / 1-3期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
vertex cover; graph matching; approximation algorithm; inapproximability;
D O I：
10.1016/j.tcs.2004.12.034
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
It has been a challenging open problem whether there is a polynomial time approximation algorithm for the VERTEX COVER problem whose approximation ratio is bounded by a constant less than 2. In this paper, we study the VERTEX COVER problem on graphs with perfect matching (shortly, VC-PM). We show that if the VC-PM problem has a polynomial time approximation algorithm with approximation ratio bounded by a constant less than 2, then so does the VERTEX COVER problem on general graphs. Approximation algorithms for VC-PM are developed, which induce improvements over previously known algorithms on sparse graphs. For example, for graphs of average degree 5, the approximation ratio of our algorithm is 1.414, compared with the previously best ratio 1.615 by Halldorsson and Radhakrishnan. (c) 2005 Elsevier B.V. All rights reserved.
引用
收藏
页码：305 / 318
页数：14
相关论文
共 50 条
  • [31] Minimum k-Path Vertex Cover in Cartesian Product Graphs
    Huiling YIN
    Binbin HAO
    Xiaoyan SU
    Jingrong CHEN
    Journal of Mathematical Research with Applications, 2021, 41 (04) : 340 - 348
  • [32] Approximated Distributed Minimum Vertex Cover Algorithms for Bounded Degree Graphs
    Zhang, Yong
    Chin, Francis Y. L.
    Ting, Hing-Fung
    COMPUTING AND COMBINATORICS, 2010, 6196 : 100 - +
  • [33] Local Search with Noisy Strategy for Minimum Vertex Cover in Massive Graphs
    Ma, Zongjie
    Fan, Yi
    Su, Kaile
    Li, Chengqian
    Sattar, Abdul
    PRICAI 2016: TRENDS IN ARTIFICIAL INTELLIGENCE, 2016, 9810 : 283 - 294
  • [34] A Breadth First Search Approach For Minimum Vertex Cover of Grid Graphs
    Angel, D.
    PROCEEDINGS OF 2015 IEEE 9TH INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS AND CONTROL (ISCO), 2015,
  • [35] Approximating the minimum clique cover and other hard problems in subtree filament graphs
    Keil, J. Mark
    Stewart, Lorna
    DISCRETE APPLIED MATHEMATICS, 2006, 154 (14) : 1983 - 1995
  • [36] Minimum weighted clique cover on claw-free perfect graphs
    Bonomo, Flavia
    Oriolo, Gianpaolo
    Snels, Claudia
    JOURNAL OF GRAPH THEORY, 2021, 96 (02) : 231 - 268
  • [37] Minimum Weighted Clique Cover on Strip-Composed Perfect Graphs
    Bonomo, Flavia
    Oriolo, Gianpaolo
    Snels, Claudia
    GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE, 2012, 7551 : 22 - 33
  • [38] Stochastic Minimum Vertex Cover in General Graphs: A 3/2-Approximation
    Derakhshan, Mahsa
    Durvasula, Naveen
    Haghtalab, Nika
    PROCEEDINGS OF THE 55TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC 2023, 2023, : 242 - 253
  • [39] Minimum vertex cover in generalized random graphs with power law degree distribution
    Vignatti, Andre L.
    da Silva, Murilo V. G.
    THEORETICAL COMPUTER SCIENCE, 2016, 647 : 101 - 111
  • [40] Towards faster local search for minimum weight vertex cover on massive graphs
    Cai, Shaowei
    Li, Yuanjie
    Hou, Wenying
    Wang, Haoran
    INFORMATION SCIENCES, 2019, 471 : 64 - 79
12345