Multi-coloring Trees

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-completiontimes 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 polynomialtime approximation scheme for the preemptive case.

• Type: Conference
• Year: 1999
• Where: COCOON
• Authors: Magnús M. Halldórsson, Guy Kortsarz, Andrzej Proskurowski, Ravit Salman, Hadas Shachnai, Jan Arne Telle
• Keywords: COCOON 1999, Combinatorics, Graph Multicoloring Problem, Multicoloring Problem, Non-preemptive Case