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Closing the Gap for Single Resource Constraint Scheduling

Authors Klaus Jansen , Malin Rau

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Author Details

Klaus Jansen
  • Universität Kiel, Germany
Malin Rau
  • Universität Hamburg, Germany

Funding

Research was supported by German Research Foundation (DFG) project JA 612 / 20-1.

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Klaus Jansen and Malin Rau. Closing the Gap for Single Resource Constraint Scheduling. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ESA.2021.53

Abstract

In the problem called single resource constraint scheduling, we are given m identical machines and a set of jobs, each needing one machine to be processed as well as a share of a limited renewable resource R. A schedule of these jobs is feasible if, at each point in the schedule, the number of machines and resources required by jobs processed at this time is not exceeded. It is NP-hard to approximate this problem with a ratio better than 3/2. On the other hand, the best algorithm so far has an absolute approximation ratio of 2+ε. In this paper, we present an algorithm with absolute approximation ratio (3/2+ε), which closes the gap between inapproximability and best algorithm with exception of a negligible small ε.

Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Theory of computation → Scheduling algorithms
Keywords
  • resource constraint scheduling
  • approximation algorithm

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