Job shop scheduling with unit processing times

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