License: 
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2012.185
URN: urn:nbn:de:0030-drops-38576
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3857/
Khandekar, Rohit ;
Hildrum, Kirsten ;
Rajan, Deepak ;
Wolf, Joel
Scheduling with Setup Costs and Monotone Penalties
Abstract
We consider single processor preemptive scheduling with job-dependent setup times. In this model, a job-dependent setup time is incurred when a job is started for the first time, and each time it is restarted after preemption. This model is a common generalization of preemptive scheduling, and actually of non-preemptive scheduling as well. The objective is to minimize the sum of any general non-negative, non-decreasing cost functions of the completion times of the jobs -- this generalizes objectives of minimizing weighted flow time, flow-time squared, tardiness or the number of tardy jobs among many others. Our main result is a randomized polynomial time O(1)-speed O(1)-approximation algorithm for this problem. Without speedup, no polynomial time finite multiplicative approximation is possible unless P=NP.
We extend the approach of Bansal et al. (FOCS 2007) of rounding a linear programming relaxation which accounts for costs incurred due to the non-preemptive nature of the schedule. A key new idea used in the rounding is that a point in the intersection polytope of two matroids can be decomposed as a convex combination of incidence vectors of sets that are independent in both matroids. In fact, we use this for the intersection of a partition matroid and a laminar matroid, in which case the decomposition can be found efficiently using network flows.
Our approach gives a randomized polynomial time offline O(1)-speed O(1)-approximation algorithm for the broadcast scheduling problem with general cost functions as well.
BibTeX - Entry
@InProceedings{khandekar_et_al:LIPIcs:2012:3857,
author = {Rohit Khandekar and Kirsten Hildrum and Deepak Rajan and Joel Wolf},
title = {{Scheduling with Setup Costs and Monotone Penalties}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) },
pages = {185--198},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-47-7},
ISSN = {1868-8969},
year = {2012},
volume = {18},
editor = {Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2012/3857},
URN = {urn:nbn:de:0030-drops-38576},
doi = {10.4230/LIPIcs.FSTTCS.2012.185},
annote = {Keywords: Scheduling, resource augmentation, approximation algorithm, preemption, setup times}
}
|
Keywords: |
|
Scheduling, resource augmentation, approximation algorithm, preemption, setup times |
|
Collection: |
|
IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) |
|
Issue Date: |
|
2012 |
|
Date of publication: |
|
14.12.2012 |
