Abstract
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(g 1 − 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.
This work was supported in part by the NSF of China under Grant No. 70221001 and 60373012.
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Chen, X., Hu, X., Jia, X. (2005). Complexity of Minimal Tree Routing and Coloring. In: Megiddo, N., Xu, Y., Zhu, B. (eds) Algorithmic Applications in Management. AAIM 2005. Lecture Notes in Computer Science, vol 3521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496199_3
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DOI: https://doi.org/10.1007/11496199_3
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