LATIN 2006: Theoretical Informatics

Abstract

We study an online job scheduling problem arising in networks with aggregated links. The goal is to schedule n jobs, divided into k disjoint chains, on m identical machines, without preemption, so that the jobs within each chain complete in the order of release times and the maximum flow time is minimized. We present a deterministic online algorithm Block with competitive ratio O(√n/m), and show a matching lower bound, even for randomised algorithms. The performance bound for Block we derive in the paper is, in fact, more subtle than a simple competitive analysis, and it shows that in overload conditions (when many jobs are released in a short amount of time), Block's performance is close to the optimum. We also show efficient offline algorithms to minimize maximum flow time and makespan in our model for k = 1, and prove that minimizing the maximum flow time and makespan for κ, m ≥ 2 is NP-hard. © Springer-Verlag Berlin Heidelberg 2006.