Linear Time Algorithms for Multiple Cluster Scheduling and Multiple Strip Packing

Abstract

We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than 2 unless In this paper, we present an algorithm with approximation ratio 2 and running time for both problems for (and running time While a 2 approximation was known before, the running time of the algorithm is at least in the worst case. Therefore, an algorithm is surprising and the best possible. While the above result is strong from a theoretical point of view, it might not be very practical due to a large hidden constant caused by calling an AEPTAS with a constant as subroutine. Nevertheless, we point out that the general approach of finding first a schedule on one cluster and then distributing it onto the other clusters might come in handy in practical approaches. We demonstrate this by presenting a practical algorithm with running time without hidden constants, that is an approximation algorithm with ratio 9/4 if the number N of clusters is dividable by 3 and bounded by otherwise.