Multi-coloring trees

Authors:
Magnús M. Halldórsson;Guy Kortsarz;Andrzej Proskurowski;Ravit Salman;Hadas Shachnai;Jan Arne Telle
Affiliations:
Science Institute, University of Iceland, Reykjavik, Iceland and Department of Informatics, University of Bergen, Bergen, Norway;Dept. of Computer Science, Open University, Ramat Aviv, Israel;Dept. of Computer Science, University of Oregon, Eugene, Oregon;Dept. of Mathematics, Technion, Haifa, Israel;Dept. of Computer Science, Technion, Haifa, Israel;Dept. of Informatics, University of Bergen, Bergen, Norway
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

Scheduling jobs with pairwise conflicts is modeled by the graph multi-coloring problem. It occurs in two versions: preemptive and non-preemptive. We study these problems on trees under the sum-of-completion-times objective. In particular, we give a quadratic algorithm for the non-preemptive case, and a faster algorithm in the case that all job lengths are short, while we present a polynomial-time approximation scheme for the preemptive case.