Path-independent load balancing with unreliable machines

Abstract

We consider algorithms for load balancing on unreliable machines. The objective is to optimize the two criteria of minimizing the makespan and minimizing job reassignments in response to machine failures. We assume that the set of jobs is known in advance but that the pattern of machine failures is unpredictable. Motivated by the requirements of BGP routing, we consider path-independent algorithms, with the property that the job assignment is completely determined by the subset of available machines and not the previous history of the assignments. We examine first the question of performance measurement of path-independent load-balancing algorithms, giving the measure of makespan and the normalized measure of reassignments cost. We then describe two classes of algorithms for optimizing these measures against an oblivious adversary for identical machines. The first, based on independent random assignments, gives expected reassignment costs within a factor of 2 of optimal and gives a makespan within a factor of O(log m/log log m) of optimal with high probability, for unknown job sizes. The second, in which jobs are first grouped into bins and at most one bin is assigned to each machine, gives constant-factor ratios on both reassignment cost and makespan, for known job sizes. Several open problems are discussed.