# Applications of parallel scheduling to perfect graphs

Parallelism And Distributed Systems

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## Abstract

We combine a parallel algorithm for the two processor scheduling problem, which runs in polylog time on a polynomial number of processors, with an algorithm to find transitive orientations of graphs where they exist. Both algorithms together solve the maximum clique problem and the minimum coloring problem for comparability graphs, and the maximum matching problem for co-comparability graphs. These parallel algorithms can also be used to identify permutation graphs and interval graphs, important subclasses of perfect graphs.

## Keywords

Optimal Schedule Precedence Constraint Interval Graph Comparability Graph Maximum Match
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1987