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Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines

Authors George Karakostas, Stavros G. Kolliopoulos

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Author Details

George Karakostas
  • Department of Computing & Software, McMaster University, Hamilton, Canada
Stavros G. Kolliopoulos
  • Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece

Funding

  • Kolliopoulos, Stavros G.: Travel support was provided by the Faculty of Science of the National and Kapodistrian University of Athens.

Cite AsGet BibTex

George Karakostas and Stavros G. Kolliopoulos. Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.5

Abstract

We study the classic weighted maximum throughput problem on unrelated machines. We give a (1-1/e-ε)-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ρ-approximation algorithm for the single-machine problem to obtain an approximation factor of (1-1/e)ρ -ε for the corresponding unrelated-machines problem, for any ε > 0. On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1-1/e) -ε for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • scheduling
  • maximum weighted throughput
  • unrelated machines
  • approximation algorithm
  • PTAS

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