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


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.

ホスト出版物のタイトルFrontiers in Algorithmics - 4th International Workshop, FAW 2010, Proceedings
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


名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
6213 LNCS


Other4th International Frontiers of Algorithmics Workshop, FAW 2010

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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