Departmental Papers (CIS)

Document Type

Conference Paper

Date of this Version

July 2001

Comments

Postprint version. Published in Lecture Notes in Computer Science, Volume 2076, Automata, Languages, and Programming, (ICALP 2001), pages 848-861.
Publisher URL: http://springerlink.metapress.com/link.asp?id=105633

Abstract

We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine is specified by an arbitrary vector) at the other end. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms are known for even the most general machine environment of unrelated machines. Recently a PTAS was discovered for the case of identical parallel machines [1]. In contrast, the problem is MAX SNP-hard for unrelated machines [11]. An important open problem was to determine the approximability of the intermediate case of uniformly related machines where each machine has a speed and it takes p/s time to process a job of size p on a machine with speed s. We resolve the complexity of this problem by obtaining a PTAS. This improves the earlier known approximation ratio of (2 + ε).

Keywords

polynomial time approximation scheme, average completion time, scheduling, uniformly related machines, weighted completion time

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Date Posted: 23 December 2005