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 that is of independent interest.
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