Purely combinatorial approximation algorithms for maximum k-vertex cover in bipartite graphs

被引：3

作者：

Bonnet, Edouard ^{[1
]}

Escoffier, Bruno ^{[2
]}

Paschos, Vangelis Th. ^{[3
]}

Stamoulis, Georgios ^{[4
]}

机构：

[1] Middlesex Univ, Dept Comp Sci, London, England

[2] UPMC Univ Paris 6, CNRS, Sorbonne Univ, LIP6,UMR 7606, Paris, France

[3] PSL Res Univ, Univ Paris Dauphine, CNRS, UMR 7243,LAMSADE, F-75016 Paris, France

[4] Maastricht Univ, Dept Data Sci & Knowledge Engn, Maastricht, Netherlands

来源：

DISCRETE OPTIMIZATION | 2018年 / 27卷

基金：

新加坡国家研究基金会;

关键词：

Approximation algorithms; Combinatorial algorithms; Non linear program; Graph algorithms; Maximum coverage; MAX-CUT;

D O I：

10.1016/j.disopt.2017.09.001

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We study the polynomial time approximation of the NP-hard MAX k-VERTEX COVER problem in bipartite graphs and propose purely combinatorial approximation algorithms . The main result of the paper is a simple combinatorial algorithm and a computer-assisted analysis of its approximation guarantee giving strong evidence that the worst approximation ratio achieved is bounded below by 0.821. We also study two simpler strategies with provable approximation ratios of 2/3 and 34/47 approximate to 0.72 respectively that already beat the only such known algorithm, namely the greedy approach which guarantees ratio (1-1/e) approximate to 0.632. Our principal motivation is to bring a satisfactory answer in the following question: to what extent combinatorial methods for MAX k-VERTEX COVEr compete with linear programming ones? (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：26 / 56

页数：31

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