NDLI: Convex quadratic and semidefinite programming relaxations in scheduling

Content Provider	ACM Digital Library
Author	Skutella, Martin
Copyright Year	2001
Abstract	We consider the problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs. The main contribution of this paper is a provably good convex quadratic programming relaxation of strongly polynomial size for this problem. The best previously known approximation algorithms are based on LP relaxations in time- or interval-indexed variables. Those LP relaxations, however, suffer from a huge number of variables. As a result of the convex quadratic programming approach we can give a very simple and easy to analyze 2-approximation algorithm which can be further improved to performance guarantee 3/2 in the absence of release dates. We also consider preemptive scheduling problems and derive approximation algorithms and results on the power of preemption which improve upon the best previously known results for these settings. Finally, for the special case of two machines we introduce a more sophisticated semidefinite programming relaxation and apply the random hyperplane technique introduced by Goemans and Williamson for the MaxCut problem; this leads to an improved 1.2752-approximation.
Starting Page	206
Ending Page	242
Page Count	37
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/375827.375840
Journal	Journal of the ACM (JACM)
Volume Number	48
Issue Number	2
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2001-03-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Approximation algorithms Convex optimization Performance guarantee Randomized algorithms Scheduling theory Unrelated machines Worst-case ratio
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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