Publication IEICE TRANSACTIONS on Information and SystemsVol.E89-DNo.8pp.2405-2410 Publication Date: 2006/08/01 Online ISSN: 1745-1361 DOI: 10.1093/ietisy/e89-d.8.2405 Print ISSN: 0916-8532 Type of Manuscript: INVITED PAPER (Special Section on Invited Papers from New Horizons in Computing) Category: Keyword: approximation algorithm, vertex cover, perfect matching, MAX-2SAT,
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Summary: Chen and Kanj considered the VERTEX COVER problem for graphs with perfect matchings (VC-PM). They showed that: (i) There is a reduction from general VERTEX COVER to VC-PM, which guarantees that if one can achieve an approximation factor of less than two for VC-PM, then one can do so for general VERTEX COVER as well. (ii) There is an algorithm for VC-PM whose approximation factor is given as 1.069+0.069 where is the average degree of the given graph. In this paper we improve (ii). Namely we give a new VC-PM algorithm which greatly outperforms the above one and its approximation factor is roughly . Our algorithm also works for graphs with "large" matchings, although its approximation factor is degenerated.