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An NC Parallel Algorithm for Edge-Coloring Series–Parallel Multigraphs

✍ Scribed by Xiao Zhou; Hitoshi Suzuki; Takao Nishizeki

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
254 KB
Volume
23
Category
Article
ISSN
0196-6774

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✦ Synopsis

Many combinatorial problems can be efficiently solved in parallel for series᎐parallel multigraphs. The edge-coloring problem is one of a few combinatorial problems for which no NC parallel algorithm has been obtained for series᎐parallel multigraphs. This paper gives an NC parallel algorithm for the Ž . Ž . problem on series᎐parallel multigraphs G. It takes O log n time with O ⌬ nrlog n processors, where n is the number of vertices and ⌬ is the maximum degree of G.

📜 SIMILAR VOLUMES

A Linear Algorithm for Edge-Coloring Ser
A Linear Algorithm for Edge-Coloring Series–Parallel Multigraphs
✍ Xiao Zhou; Hitoshi Suzuki; Takao Nishizeki 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 313 KB

Many combinatorial problems can be efficiently solved for series᎐parallel multigraphs. However, the edge-coloring problem of finding the minimum number of colors required for edge-coloring given graphs is one of a few well-known combinatorial problems for which no efficient algorithms have been obta

Parallel Algorithms for the Edge-Colorin
Parallel Algorithms for the Edge-Coloring and Edge-Coloring Update Problems
✍ Weifa Liang; Xiaojun Shen; Qing Hu 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 342 KB

In fact, Vizing's proof implies an O(nm) time algorithm with ⌬ ϩ 1 colors for the edge-coloring problem. However, Holyer has shown that deciding whether a graph requires ⌬ or ⌬ ϩ 1 colors is NP-complete [10]. For a multigraph G, Shannon showed that Ј(G) Յ 3⌬/2 [16]. A number of parallel algorithms