Multicoloring trees

Authors:
Magnús M. Halldórsson;Guy Kortsarz;Andrzej Proskurowski;Ravit Salman;Hadas Shachnai;Jan Arne Telle
Affiliations:
Department of Computer Science, University of Iceland, IS-107 Reykjavik, Iceland;Department of Computer Science, Rutgers University, Camden, NJ;Department of Computer Science, University of Oregon, Eugene, OR;Department of Mathematics, Technion, Haifa 32000 Israel;Department of Computer Science, Technion, Haifa 32000 Israel;Department of Informatics, University of Bergen, Bergen, Norway
Venue:
Information and Computation
Year:
2003

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Abstract

Scheduling jobs with pairwise conflicts is modeled by the graph multicoloring problem. It occurs in two versions: in the preemptive case, each vertex may get any set of colors, while in the non-preemptive case, the set of colors assigned to each vertex has to be contiguous. We study these versions of the multicoloring problem 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.