Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines

Authors George Karakostas, Stavros G. Kolliopoulos

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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

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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)


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
  • scheduling
  • maximum weighted throughput
  • unrelated machines
  • approximation algorithm
  • PTAS


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