Randomized on-line and semi-on-line scheduling on identical machines

This paper considers on-line and semi-on-line scheduling problems on m parallel machines with objective to maximize the minimum load. For on-line version, we prove that algorithm Random is an optimal randomized algorithm on two machines, and derive a new randomized upper bound for general m machines which significantly improves the known upper bound. For semi-on-line version with non-increasing job processing times, we show that LS algorithm is an optimal deterministic algorithm for two and three machine cases. We further present an optimal randomized algorithm RLS for two machine case.