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
A Linear Algorithm for Edge-Coloring Series–Parallel Multigraphs
✍ Scribed by Xiao Zhou; Hitoshi Suzuki; Takao Nishizeki
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 313 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0196-6774
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✦ Synopsis
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 obtained for series᎐parallel multigraphs. This paper gives a linear algorithm for the problem on series᎐parallel multigraphs.
📜 SIMILAR VOLUMES
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
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