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Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.37
An Efficient PTAS for Stochastic Load Balancing with Poisson Jobs

Authors: Anindya De, Sanjeev Khanna, Huan Li, and Hesam Nikpey

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We give the first polynomial-time approximation scheme (PTAS) for the stochastic load balancing problem when the job sizes follow Poisson distributions. This improves upon the 2-approximation algorithm due to Goel and Indyk (FOCS'99). Moreover, our approximation scheme is an efficient PTAS that has a running time double exponential in 1/ε but nearly-linear in n, where n is the number of jobs and ε is the target error. Previously, a PTAS (not efficient) was only known for jobs that obey exponential distributions (Goel and Indyk, FOCS'99). Our algorithm relies on several probabilistic ingredients including some (seemingly) new results on scaling and the so-called "focusing effect" of maximum of Poisson random variables which might be of independent interest.
Cite as

Anindya De, Sanjeev Khanna, Huan Li, and Hesam Nikpey. An Efficient PTAS for Stochastic Load Balancing with Poisson Jobs. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{de_et_al:LIPIcs.ICALP.2020.37,
  author =	{De, Anindya and Khanna, Sanjeev and Li, Huan and Nikpey, Hesam},
  title =	{{An Efficient PTAS for Stochastic Load Balancing with Poisson Jobs}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.37},
  URN =		{urn:nbn:de:0030-drops-124449},
  doi =		{10.4230/LIPIcs.ICALP.2020.37},
  annote =	{Keywords: Efficient PTAS, Makespan Minimization, Scheduling, Stochastic Load Balancing, Poisson Distribution}
}
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