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DOI: 10.4230/LIPIcs.FSTTCS.2012.185
URN: urn:nbn:de:0030-drops-38576
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Khandekar, Rohit ; Hildrum, Kirsten ; Rajan, Deepak ; Wolf, Joel

Scheduling with Setup Costs and Monotone Penalties

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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

  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 =		{},
  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

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