Bi-Criteria Approximation Algorithms for Load Balancing on Unrelated Machines with Costs

Authors Trung Thanh Nguyen, Jörg Rothe

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Author Details

Trung Thanh Nguyen
  • ORLab, Faculty of Computer Science, Phenikaa University, Hanoi 12116, Vietnam
Jörg Rothe
  • Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, Germany


We thank the anonymous ISAAC 2020 reviewers for helpful comments.

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Trung Thanh Nguyen and Jörg Rothe. Bi-Criteria Approximation Algorithms for Load Balancing on Unrelated Machines with Costs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We study a generalized version of the load balancing problem on unrelated machines with cost constraints: Given a set of m machines (of certain types) and a set of n jobs, each job j processed on machine i requires p_{i,j} time units and incurs a cost c_{i,j}, and the goal is to find a schedule of jobs to machines, which is defined as an ordered partition of n jobs into m disjoint subsets, in such a way that some objective function of the vector of the completion times of the machines is optimized, subject to the constraint that the total costs by the schedule must be within a given budget B. Motivated by recent results from the literature, our focus is on the case when the number of machine types is a fixed constant and we develop a bi-criteria approximation scheme for the studied problem. Our result generalizes several known results for certain special cases, such as the case with identical machines, or the case with a constant number of machines with cost constraints. Building on the elegant technique recently proposed by Jansen and Maack [K. Jansen and M. Maack, 2019], we construct a more general approach that can be used to derive approximation schemes to a wider class of load balancing problems with constraints.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • bi-criteria approximation algorithm
  • polynomial-time approximation algorithm
  • load balancing
  • machine scheduling


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