Volume 1284 of the series Lecture Notes in Computer Science pp 416429
SchedulingLPs bear probabilities randomized approximations for minsum criteria
 Andreas S. SchulzAffiliated withFachbereich Mathematik, Technische Universität Berlin
 , Martin SkutellaAffiliated withFachbereich Mathematik, Technische Universität Berlin
Abstract
In this paper, we provide a new class of randomized approximation algorithms for scheduling problems by directly interpreting solutions to socalled timeindexed LPs as probabilities. The most general model we consider is scheduling unrelated parallel machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. The crucial idea for these multiple machine problems is not to use standard list scheduling but rather to assign jobs randomly to machines (with probabilities taken from an optimal LP solution) and to perform list scheduling on each of them.
For the general model, we give a (2+ E)approximation algorithm. The best previously known approximation algorithm has a performance guarantee of 16/3 [HSW96]. Moreover, our algorithm also improves upon the best previously known approximation algorithms for the special case of identical parallel machine scheduling (performance guarantee (2.89 + E) in general [CPS+96] and 2.85 for the average completion time [CMNS97], respectively). A perhaps surprising implication for identical parallel machines is that jobs are randomly assigned to machines, in which each machine is equally likely. In addition, in this case the algorithm has running time O(nlogn) and performance guarantee 2. The same algorithm also is a 2approximation for the corresponding preemptive scheduling problem on identical parallel machines.
Finally, the results for identical parallel machine scheduling apply to both the offline and the online settings with no difference in performance guarantees. In the online setting, we are scheduling jobs that continually arrive to be processed and, for each time t, we must construct the schedule until time t without any knowledge of the jobs that will arrive afterwards.
 Title
 SchedulingLPs bear probabilities randomized approximations for minsum criteria
 Book Title
 Algorithms — ESA '97
 Book Subtitle
 5th Annual European Symposium Graz, Austria, September 15–17, 1997 Proceedings
 Pages
 pp 416429
 Copyright
 1997
 DOI
 10.1007/3540633979_32
 Print ISBN
 9783540633976
 Online ISBN
 9783540695363
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1284
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Andreas S. Schulz ^{(1)}
 Martin Skutella ^{(1)}
 Author Affiliations

 1. Fachbereich Mathematik, Technische Universität Berlin, MA 61, Straße des 17. Juni 136, 10623, Berlin, Germany
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