A 2-approximation algorithm for path coloring on a restricted class of trees of rings

Authors:
Xiaotie Deng;Guojun Li;Wenan Zang;Yi Zhou
Affiliations:
Department of Computer Science, City University of Hong Kong, Hong Kong, PR China;Department of Mathematics, Shandong University, Jinan 250100, PR China;Department of Mathematics, The University of Hong Kong, Hong Kong, PR China;Department of Computer Science, City University of Hong Kong, Hong Kong, PR China
Venue:
Journal of Algorithms
Year:
2003

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Abstract

A tree of rings is an undirected graph obtained from a tree by replacing each node of the tree with a cycle (called tree-node-cycle) and then contracting the edges of the tree so that two cycles corresponding to the two end-nodes of any edge have precisely one node in common and no three tree-node-cycles share a same node. (A more general definition may allow them to share the same node.) Given a set of paths on a tree of rings, the path coloring problem is to color these paths with the smallest number of colors so that any two paths sharing an edge are assigned different colors. In this paper, we present a 2-approximation algorithm for this problem.