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An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time 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 objective

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Abstract

We study a classic scheduling problem on uniformly related machines for which we show an efficient polynomial time approximation scheme (EPTAS), where an EPTAS is a fast and practical approximation scheme. For a desired approximation ratio of 1+ε for ε > 0, the running time of an EPTAS is a function of ε multiplied by a polynomial function of the input length. New methods and techniques are essential in developing such improved approximation schemes, and their design is a primary goal of this research agenda. We present an EPTAS for the scheduling problem of a set of jobs on uniformly related machines so as to minimize the total weighted completion time. The problem is NP-hard in the strong sense, and therefore an EPTAS is the best possible approximation scheme for the problem, unless P=NP. Prior to our work, only a PTAS was known for the problem, while an EPTAS was known only for the special case of identical machines.

Cite As Get BibTex

Leah Epstein and Asaf Levin. An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time on Uniformly Related Machines. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 25:1-25:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.25

Author Details

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

Funding

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

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