Complexity of Minimal Tree Routing and Coloring

Let G be a undirected connected graph. Given a set of g groups each being a subset of V (G), tree routing and coloring 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 how to find a tree routing and coloring that uses minimal number of colors, which finds an application of setting up multicast connections in optical networks. We first prove Ω(g1−ε )-inapproximability of the problem even when G is a mesh, and then we propose some approximation algorithms with provable performance guarantees for general graphs and some special graphs as well.

• Type: Conference
• Year: 2005
• Where: AAIM
• Authors: Xujin Chen, Xiao-Dong Hu, Xiaohua Jia
• Keywords: AAIM 2005, Algorithms, Provable Performance Guarantees, Tree Routing, Undirected Connected Graph