Scheduling problem subject to compatibility constraints

Abstract

The problem studied in this paper consists in finding the minimum makespan in a problem of scheduling jobs on identical parallel processors subject to compatibility constraints that some jobs cannot be scheduled simultaneously in any time interval. These constraints are modeled by a graph in which compatible jobs are represented by adjacent vertices. We study the complexity of this problem for bipartite graphs and their complements. We propose polynomial heuristics which are ex- perimentally evaluated and compared