Parallel Edge Coloring of a Tree on a Mesh Connected Computer

Authors:
Chang-Sung Jeong;Sung-Up Cho;Sun-Chul Whang;Mi-Young Choi
Affiliations:
-;-;-;-
Venue:
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Year:
2000

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Abstract

An edge coloring is an assignment of colors to the edges of a graph so that no two edges with a common vertex have the same color. We show that, given an undirected tree T with n vertices, a minimum edge coloring of T can be determined in O(√n) time on a √n × √n mesh-connected computer(MCC) by a novel technique which decomposes the tree into disjoint chains and then assigns the edge colors in each chain properly. The time complexity is optimal on MCC within constant factor.