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Optimally Handling Commitment Issues in Online Throughput Maximization

Authors Franziska Eberle , Nicole Megow , Kevin Schewior

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Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Scheduling algorithms
Keywords
  • Deadline scheduling
  • throughput
  • online algorithms
  • competitive analysis

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Abstract

We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on m machines that maximizes the number of jobs that complete before their deadline. Due to strong impossibility results for competitive analysis, it is commonly required that jobs contain some slack ε > 0, which means that the feasible time window for scheduling a job is at least 1+ε times its processing time. In this paper, we answer the question on how to handle commitment requirements which enforce that a scheduler has to guarantee at a certain point in time the completion of admitted jobs. This is very relevant, e.g., in providing cloud-computing services and disallows last-minute rejections of critical tasks. We present the first online algorithm for handling commitment on parallel machines for arbitrary slack ε. When the scheduler must commit upon starting a job, the algorithm is Θ(1/ε)-competitive. Somewhat surprisingly, this is the same optimal performance bound (up to constants) as for scheduling without commitment on a single machine. If commitment decisions must be made before a job’s slack becomes less than a δ-fraction of its size, we prove a competitive ratio of 𝒪(1/(ε - δ)) for 0 < δ < ε. This result nicely interpolates between commitment upon starting a job and commitment upon arrival. For the latter commitment model, it is known that no (randomized) online algorithms admits any bounded competitive ratio.

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Franziska Eberle, Nicole Megow, and Kevin Schewior. Optimally Handling Commitment Issues in Online Throughput Maximization. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 41:1-41:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ESA.2020.41

Author Details

Franziska Eberle
  • Department for Mathematics and Computer Science, University of Bremen, Germany
Nicole Megow
  • Department for Mathematics and Computer Science, University of Bremen, Germany
Kevin Schewior
  • Universität zu Köln, Department of Mathematics and Computer Science, Germany

Funding

  • Megow, Nicole: Partially supported by the German Science Foundation (DFG) under contract ME 3825/1.
  • Schewior, Kevin: Partially supported by the DAAD within the PRIME program using funds of BMBF and the EU Marie Curie Actions.

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