Randomized algorithms for on-line scheduling problems: how low can't you go?

vVe prove lower bounds on the competitive ratio of randomized algorithms for several on-line scheduling problems. The main result is a bound of ej(e 1) for the on-line problem with objective minimizing the sum of completion times of jobs that arrive over time at their release times and are to be processed on a single machine. This lower bound shows that a randomized algorithm designed in [Chekuri et al. 19971 is a best possible randomized algorithm for this problem.