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Scheduling on a Stochastic Number of Machines

Authors Moritz Buchem , Franziska Eberle , Hugo Kooki Kasuya Rosado , Kevin Schewior , Andreas Wiese

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ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • scheduling
  • approximation algorithms
  • stochastic machines
  • makespan
  • max-min fair allocation
  • dynamic programming

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Abstract

We consider a new scheduling problem on parallel identical machines in which the number of machines is initially not known, but it follows a given probability distribution. Only after all jobs are assigned to a given number of bags, the actual number of machines is revealed. Subsequently, the jobs need to be assigned to the machines without splitting the bags. This is the stochastic version of a related problem introduced by Stein and Zhong [SODA 2018, TALG 2020] and it is, for example, motivated by bundling jobs that need to be scheduled by data centers. We present two PTASs for the stochastic setting, computing job-to-bag assignments that (i) minimize the expected maximum machine load and (ii) maximize the expected minimum machine load (like in the Santa Claus problem), respectively. The former result follows by careful enumeration combined with known PTASs. For the latter result, we introduce an intricate dynamic program that we apply to a suitably rounded instance.

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Moritz Buchem, Franziska Eberle, Hugo Kooki Kasuya Rosado, Kevin Schewior, and Andreas Wiese. Scheduling on a Stochastic Number of Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.14

Author Details

Moritz Buchem
  • Technische Universität München, Germany
Franziska Eberle
  • Technische Universität Berlin, Germany
Hugo Kooki Kasuya Rosado
  • Technische Universität München, Germany
Kevin Schewior
  • University of Southern Denmark, Odense, Denmark
Andreas Wiese
  • Technische Universität München, Germany

Funding

  • Eberle, Franziska: Supported by the Dutch Research Council (NWO), Netherlands Vidi grant 016.Vidi.189.087.
  • Schewior, Kevin: Supported by the Independent Research Fund Denmark, Natural Sciences, grant DFF-0135-00018B.

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