Abstract
Applications of Parallel Scheduling Algorithms to Families of Perfect Graphs. 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. The transitive orientation algorithm can also be used to identify permutation graphs, another important subclass of perfect graphs. AMS Subject Classifications: 68C15, 68E10, 68Q10.Key wordsTwo processor schedulingmaximum cliquemaximum matchingtransitive orientation
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