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APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.5
Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines

Authors: George Karakostas and Stavros G. Kolliopoulos

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

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.
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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)

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@InProceedings{karakostas_et_al:LIPIcs.APPROX/RANDOM.2023.5,
  author =	{Karakostas, George and Kolliopoulos, Stavros G.},
  title =	{{Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.5},
  URN =		{urn:nbn:de:0030-drops-188305},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.5},
  annote =	{Keywords: scheduling, maximum weighted throughput, unrelated machines, approximation algorithm, PTAS}
}
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