Randombased scheduling new approximations and LP lower bounds
 Andreas S. Schulz,
 Martin Skutella
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Abstract
Three characteristics encountered frequently in realworld machine scheduling are jobs released over time, precedence constraints between jobs, and average performance optimization. The general constrained onemachine scheduling problem to minimize the average weighted completion time not only captures these features, but also is an important building block for more complex problems involving multiple machines.
In this context, the conversion of preemptive to nonpreemptive schedules has been established as a strong and useful tool for the design of approximation algorithms.
The preemptive problem is already NPhard, but one can generate good preemptive schedules from LP relaxations in timeindexed variables. However, a straightforward combination of these two components does not directly lead to improved approximations. By showing schedules in slow motion, we introduce a new point of view on the generation of preemptive schedules from LPsolutions which also enables us to give a better analysis.
Specifically, this leads to a randomized approximation algorithm for the general constrained onemachine scheduling problem with expected performance guarantee e. This improves upon the best previously known worstcase bound of 3. In the process, we also give randomized algorithms for related problems involving precedences that asymptotically match the best previously known performance guarantees.
In addition, by exploiting a different technique, we give a simple 3/2approximation algorithm for unrelated parallel machine scheduling to minimize the average weighted completion time. It relies on random machine assignments where these random assignments are again guided by an optimum solution to an LP relaxation. For the special case of identical parallel machines, this algorithm is as simple as the one of Kawaguchi and Kyan [KK86], but allows for a remarkably simpler analysis. Interestingly, its derandomized version actually is the algorithm of Kawaguchi and Kyan.
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 Title
 Randombased scheduling new approximations and LP lower bounds
 Book Title
 Randomization and Approximation Techniques in Computer Science
 Book Subtitle
 International Workshop RANDOM'97 Bologna, Italy, July 11–12, 1997 Proceedings
 Pages
 pp 119133
 Copyright
 1997
 DOI
 10.1007/3540632484_11
 Print ISBN
 9783540632481
 Online ISBN
 9783540692478
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1269
 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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