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An EPTAS for Minimizing the Total Weighted Completion Time of Jobs with Release Dates on Uniformly Related Machines

Authors Leah Epstein , Asaf Levin

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Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • Scheduling algorithms
  • Approximation schemes
  • Min-sum objectives

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Abstract

Scheduling of independent jobs with release dates so as to minimize the total weighted completion time is a well-known scheduling problem. Here, we study it for the classic machine environment of uniformly related machines. An efficient polynomial time approximation scheme (an EPTAS) is a family of (1+ε)-approximation algorithms where the running time is bounded by a polynomial in the input size times a function of ε > 0. For problems that are NP-hard in the strong sense, as it is the case for the problem studied here, an EPTAS is the best possible approximation scheme. We design an EPTAS for the problem by employing known techniques and introducing a large collection of new methods.

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Leah Epstein and Asaf Levin. An EPTAS for Minimizing the Total Weighted Completion Time of Jobs with Release Dates on Uniformly Related Machines. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.44

Author Details

Leah Epstein
  • Department of Mathematics, Faculty of Natural Sciences, University of Haifa, Israel
Asaf Levin
  • Faculty of Data and Decision Sciences, Technion, Haifa, Israel

Funding

  • Levin, Asaf: Partially supported by ISF - Israel Science Foundation grant number 1467/22.

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