Departmental Papers (CIS)

Date of this Version

May 2002

Document Type

Conference Paper


Copyright ACM, 2002. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC 2002), pages 297-305.
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We present the first approximation schemes for minimizing weighted flow time on a single machine with preemption. Our first result is an algorithm that computes a (1 + ε)- approximate solution for any instance of weighted flow time in O(nO(ln W ln P3) time; here P is the ratio of maximum job processing time to minimum job processing time, and W is the ratio of maximum job weight to minimum job weight. This result directly gives a quasi-PTAS for weighted flow time when P and W are poly-bounded, and a PTAS when they are both O(1). We strengthen the former result to show that in order to get a quasi-PTAS it suffices to have just one of P and W to be poly-bounded. Our result provides strong evidence to the hypothesis that the weighted flow time problem has a PTAS. We note that the problem is strongly NP-hard even when P and W are O(1). We next consider two important special cases of weighted flow time, namely, when P is O(1) and W is arbitrary, and when the weight of a job is inverse of its processing time referred to as the stretch metric. For both of the above special cases we obtain a (1 + ε)-approximation for any ε > 0 by using a randomized partitioning scheme to reduce an arbitrary instance to several instances all of which have P and W bounded by a constant that depends only on ε.



Date Posted: 10 March 2005

This document has been peer reviewed.