Complexity of minimal tree routing and coloring

Authors:
Xujin Chen;Xiaodong Hu;Xiaohua Jia
Affiliations:
Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China;Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, SAR, China
Venue:
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Year:
2005

Citing 10
Cited 0

On the 1.1 edge-coloring of multigraphs

SIAM Journal on Discrete Mathematics
A still better performance guarantee for approximate graph coloring

Information Processing Letters
Efficient routing in all-optical networks

STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results

SIAM Journal on Computing
Zero knowledge and the chromatic number

Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
The complexity of path coloring and call scheduling

Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Path coloring on the mesh

FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Routing algorithm for multicast under multi-tree model in optical networks

Theoretical Computer Science
Light trees: optical multicasting for improved performance in wavelength routed networks

IEEE Communications Magazine

Quantified Score

Hi-index	0.00

Visualization

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(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.