An approximation algorithm dependent on edge-coloring number for minimum maximal matching problem

Yusuke Matsumoto, Naoyuki Kamiyama, Keiko Imai

研究成果: Contribution to journalArticle査読

5 被引用数 (Scopus)

抄録

We consider the minimum maximal matching problem, which is NP-hard (Yannakakis and Gavril (1980) [18]). Given an unweighted simple graph G=(V,E), the problem seeks to find a maximal matching of minimum cardinality. It was unknown whether there exists a non-trivial approximation algorithm whose approximation ratio is less than 2 for any simple graph. Recently, Z. Gotthilf et al. (2008) [5] presented a (2-clog|V||V|)-approximation algorithm, where c is an arbitrary constant. In this paper, we present a (2-1 χ′(G))-approximation algorithm based on an LP relaxation, where χ′(G) is the edge-coloring number of G. Our algorithm is the first non-trivial approximation algorithm whose approximation ratio is independent of |V|. Moreover, it is known that the minimum maximal matching problem is equivalent to the edge dominating set problem. Therefore, the edge dominating set problem is also (2-1χ′(G))-approximable. From edge-coloring theory, the approximation ratio of our algorithm is 2-1Δ(G)+1, where Δ(G) represents the maximum degree of G. In our algorithm, an LP formulation for the edge dominating set problem is used. Fujito and Nagamochi (2002) [4] showed the integrality gap of the LP formulation for bipartite graphs is at least 2-1Δ(G). Moreover, χ′(G) is Δ(G) for bipartite graphs. Thus, as far as an approximation algorithm for the minimum maximal matching problem uses the LP formulation, we believe our result is the best possible.

本文言語英語
ページ(範囲)465-468
ページ数4
ジャーナルInformation Processing Letters
111
10
DOI
出版ステータス出版済み - 4 30 2011
外部発表はい

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • 信号処理
  • 情報システム
  • コンピュータ サイエンスの応用

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