Job shop scheduling with unit processing times

Nikhil Bansal, Tracy Kimbrel, Maxim Sviridenko

Abstract: We consider randomized algorithms for the preemptive job shop problem, or equivalently, the case in which all operations have unit length. We give an α-approximation for the case of two machines where α < 1.45, an improved approximation ratio of O(log m/log log m) for an arbitrary number m of machines, and the first (2+ε)-approximation for a constant number of machines. The first result is via an approximation algorithm for a string matching problem which is of independent interest.