An Approximation Algorithm for Diagnostic Test Scheduling in Multicomputer Systems
IEEE Transactions on Computers
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Easy problems for tree-decomposable graphs
Journal of Algorithms
Journal of Algorithms
Edge-chromatic sum of trees and bounded cyclicity graphs
Information Processing Letters
Cavity Matchings, Label Compressions, and Unrooted Evolutionary Trees
SIAM Journal on Computing
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
The Optimal Cost Chromatic Partition Problem for Trees and Interval Graphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
The Optimum Cost Chromatic Partition Problem
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Dedicated Scheduling of Biprocessor Tasks to Minimize Mean Flow Time
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
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Let C be a set of colors, and let ω be a cost function which assigns a real number ω(c) to each color c in C. An edge-coloring of a graph G is to color all the edges of G so that any two adjacent edges are colored with different colors. In this paper we give an efficient algorithm to find an optimal edge-coloring of a given tree T, that is, an edge-coloring f of T such that the sum of costs ω(f(e)) of colors f(e) assigned to all edges e is minimum among all edge-colorings of T. The algorithm takes time O(nΔ2) if n is the number of vertices and Δ is the maximum degree of T.