Inapproximability and approximability of minimal tree routing and coloring

Authors:
Xujin Chen;Xiaodong Hu;Xiaohua Jia
Affiliations:
Institute of Applied Mathematics, Chinese Academy of Sciences, PO Box 2734, Beijing 100080, PR China;Institute of Applied Mathematics, Chinese Academy of Sciences, PO Box 2734, Beijing 100080, PR China;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, SAR China
Venue:
Journal of Discrete Algorithms
Year:
2008

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Abstract

Let G be an undirected connected graph. Given a set of g groups each being a subset of V(G), the tree routing and coloring problem is to produce g trees in G and assign a color to each of them in such a way that all vertices in every group are connected by one of produced trees and no two trees sharing a common edge are assigned the same color. In this paper we study the problem of finding a tree routing and coloring that uses minimal number of colors in the solution. This problem has applications of multicast connections in optical networks.We first prove @W(g^1^-^@e)-inapproximability even when G is a mesh, and then we propose some approximation algorithms with guaranteed error bounds for general graphs and some special graphs as well.