Minimum cost edge-colorings of trees can be reduced to matchings

Takehiro Ito, Naoki Sakamoto, Xiao Zhou, Takao Nishizeki

研究成果: Conference contribution

抄録

Let C be a set of colors, and let ω(c) be an integer cost assigned to a color c in C. An edge-coloring of a graph G is to color all the edges of G so that any two adjacent edges are colored with different colors in C. The cost ω(f) of an edge-coloring f of G is the sum of costs ω(f(e)) of colors f(e) assigned to all edges e in G. An edge-coloring f of G is optimal if ω(f) is minimum among all edge-colorings of G. In this paper, we show that the problem of finding an optimal edge-coloring of a tree T can be simply reduced in polynomial time to the minimum weight perfect matching problem for a new bipartite graph constructed from T. The reduction immediately yields an efficient simple algorithm to find an optimal edge-coloring of T in time , where n is the number of vertices in T, Δ is the maximum degree of T, and N ω is the maximum absolute cost |ω(c)| of colors c in C. We then show that our result can be extended for multitrees.

本文言語English
ホスト出版物のタイトルFrontiers in Algorithmics - 4th International Workshop, FAW 2010, Proceedings
ページ274-284
ページ数11
DOI
出版ステータスPublished - 2010
イベント4th International Frontiers of Algorithmics Workshop, FAW 2010 - Wuhan, China
継続期間: 2010 8 112010 8 13

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
6213 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other4th International Frontiers of Algorithmics Workshop, FAW 2010
国/地域China
CityWuhan
Period10/8/1110/8/13

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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