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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.22

Scheduling Splittable Jobs on Configurable Machines

Authors: Matthew Casey, Rajmohan Rajaraman, David Stalfa, and Cheng Tan

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract

Motivated by modern architectures allowing for the partitioning of a GPU into hardware separated instances, we initiate the study of scheduling splittable jobs on configurable machines. We consider machines that can be configured into smaller instances, which we call blocks, in multiple ways, each of which is referred to as a configuration. We introduce the Configurable Machine Scheduling (cms) problem, where we are given n jobs and a set C of configurations. A schedule consists of a set of machines, each assigned some configuration in C with each block in the configuration assigned to process one job. The amount of a job’s demand that is satisfied by a block is given by an arbitrary function of the job and block. The objective is to construct a schedule using as few machines as possible. We provide a tight logarithmic factor approximation algorithm for this problem in the general setting, a factor (3 + ε) approximation algorithm for arbitrary ε > 0 when there are O(1) input configurations, and a polynomial time approximation scheme when both the number and size of configurations are O(1). Finally, we utilize a technique for finding conic integer combinations in fixed dimension to develop an optimal polynomial time algorithm in the case with O(1) jobs, O(1) blocks, and every configuration up to a given size.

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Matthew Casey, Rajmohan Rajaraman, David Stalfa, and Cheng Tan. Scheduling Splittable Jobs on Configurable Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{casey_et_al:LIPIcs.APPROX/RANDOM.2024.22,
  author =	{Casey, Matthew and Rajaraman, Rajmohan and Stalfa, David and Tan, Cheng},
  title =	{{Scheduling Splittable Jobs on Configurable Machines}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.22},
  URN =		{urn:nbn:de:0030-drops-210157},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.22},
  annote =	{Keywords: Scheduling algorithms, Approximation algorithms, Configurable machines, Splittable jobs, Linear programming}
}

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Scheduling Splittable Jobs on Configurable Machines

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