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A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling

Authors Klaus Jansen , Felix Ohnesorge

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LIPIcs.STACS.2026.56.pdf
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ACM Subject Classification
  • Theory of computation → Discrete optimization
  • Theory of computation → Parallel computing models
  • Theory of computation → Scheduling algorithms
Keywords
  • computing
  • machine scheduling
  • moldable
  • polynomial approximation

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Abstract

In moldable job scheduling, we are provided m identical machines and n jobs that can be executed on a variable number of machines. The execution time of each job depends on the number of machines assigned to execute that job. For the specific problem of monotone moldable job scheduling, jobs are assumed to have a processing time that is non-increasing in the number of machines.
The previous best-known algorithms are: (1) a Polynomial Time Approximation Scheme (PTAS) with time complexity Ω(n^{g(1/ε)}), where g(⋅) is a super-exponential function [Jansen and Thöle '08; Jansen and Land '18], (2) a Fully Polynomial Time Approximation Scheme (FPTAS) for the case of m ≥ 8n/(ε) [Jansen and Land '18], and (3) a 3/2 approximation with time complexity O(nmlog(mn)) [Wu, Zhang, and Chen '23].
We present a new practically efficient algorithm with an approximation ratio of ≈ (1.4593 + ε) and a time complexity of O(nm log 1/(ε)). Our result also applies to the contiguous variant of the problem. In addition to our theoretical results, we implement the presented algorithm and show that the practical performance is significantly better than the theoretical worst-case approximation ratio.

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Klaus Jansen and Felix Ohnesorge. A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 56:1-56:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.56

Author Details

Klaus Jansen
  • Kiel University, Germany
Felix Ohnesorge
  • Kiel University, Germany

Funding

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project number 453769249.

Supplementary Materials

References

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