Complexity of scheduling multiprocessor tasks with prespecified processor allocations
Discrete Applied Mathematics
Approximation results for the optimum cost chromatic partition problem
Journal of Algorithms
Edge-chromatic sum of trees and bounded cyclicity graphs
Information Processing Letters
Journal of Algorithms
The Complexity of Tree Multicolorings
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
The Optimum Cost Chromatic Partition Problem
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Information and Computation
Discrete Applied Mathematics
Sum edge coloring of multigraphs via configuration LP
ACM Transactions on Algorithms (TALG)
Minimum sum set coloring of trees and line graphs of trees
Discrete Applied Mathematics
On a local protocol for concurrent file transfers
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
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The edge multicoloring problem is that given a graph G and integer demands x (e) for every edge e, assign a set of x(e) colors to edge e, such that adjacent edges have disjoint sets of colors. In the minimum sum edge multicoloring problem the finish time of an edge is defined to be the highest color assigned to it. The goal is to minimize the sum of the finish times. The main result of the paper is a polynomial-time approximation scheme for minimum sum multicoloring the edges of trees. We also show that the problem is strongly NP-hard for trees, even if every demand is at most 2.