Minimizing Maximum Flowtime of Jobs with Arbitrary Parallelizability

We consider the problem of nonclairvoyantly scheduling jobs, which arrive over time and have varying sizes and degrees of parallelizability, with the objective of minimizing the maximum flow. We give essentially tight bounds on the achievable competitiveness. More specifically we show that the competitive ratio of every deterministic nonclairvoyant algorithm is high, namely Ω( √ n). But there is a simple batching algorithm that (1 + ε)speed O(log n)-competitive algorithm. And this simple batching algorithm is optimally competitive as no deterministic nonclairvoyant algorithm can be s-speed o(log n)-competitive for any constant speed s.