Constrainedness and the Phase Transition in Job Shop Scheduling

Recent research has shown the existence of a “phase transition” for many combinatorial problems. In this paper we investigate the existence of a phase transition in the job shop scheduling problem. We apply standard estimates for the constrainedness of constraint satisfaction problems to job shop problems and describe empirical results identifying a phase transition at a constrainedness level of approximately 0.2. This phase transition point is much lower than expected, both from theory and in comparison with the phase transition point empirically found for other problems. We argue that this discrepancy is due to the weakness of the independence assumption used in the estimation of constrainedness.