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Preemptive Scheduling of Equal-Length Jobs in Polynomial Time

Preemptive Scheduling of Equal-Length Jobs in Polynomial Time We study the preemptive scheduling problem of a set of n jobs with release times and equal processing times on a single machine. The objective is to minimize the sum of the weighted completion times $${\sum_{i=1}^{n}w_{i}C_{i}}$$ of the jobs. We propose for this problem the first parameterized algorithm on the number k of different weights. The runtime of the proposed algorithm is $${O\left(\left(\frac{n}{k}+1\right)^{k}n^{8}\right)}$$ and hence, the problem is polynomially solvable for any fixed number k of different weights. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

Preemptive Scheduling of Equal-Length Jobs in Polynomial Time

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References (43)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Mathematics, general; Computer Science, general
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-009-0003-z
Publisher site
See Article on Publisher Site

Abstract

We study the preemptive scheduling problem of a set of n jobs with release times and equal processing times on a single machine. The objective is to minimize the sum of the weighted completion times $${\sum_{i=1}^{n}w_{i}C_{i}}$$ of the jobs. We propose for this problem the first parameterized algorithm on the number k of different weights. The runtime of the proposed algorithm is $${O\left(\left(\frac{n}{k}+1\right)^{k}n^{8}\right)}$$ and hence, the problem is polynomially solvable for any fixed number k of different weights.

Journal

Mathematics in Computer ScienceSpringer Journals

Published: Nov 27, 2009

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