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On Minimizing Generalized Makespan on Unrelated Machines

Authors Nikhil Ayyadevara, Nikhil Bansal, Milind Prabhu

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Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • Hardness of Approximation
  • Generalized Makespan

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Abstract

We consider the Generalized Makespan Problem (GMP) on unrelated machines, where we are given n jobs and m machines and each job j has arbitrary processing time p_{ij} on machine i. Additionally, there is a general symmetric monotone norm ψ_i for each machine i, that determines the load on machine i as a function of the sizes of jobs assigned to it. The goal is to assign the jobs to minimize the maximum machine load.
Recently, Deng, Li, and Rabani [Deng et al., 2023] gave a 3 approximation for GMP when the ψ_i are top-k norms, and they ask the question whether an O(1) approximation exists for general norms ψ? We answer this negatively and show that, under natural complexity assumptions, there is some fixed constant δ > 0, such that GMP is Ω(log^δ n) hard to approximate. We also give an Ω(log^{1/2} n) integrality gap for the natural configuration LP.

Cite As Get BibTex

Nikhil Ayyadevara, Nikhil Bansal, and Milind Prabhu. On Minimizing Generalized Makespan on Unrelated Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 21:1-21:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.21

Author Details

Nikhil Ayyadevara
  • University of Michigan, Ann Arbor, MI, USA
Nikhil Bansal
  • University of Michigan, Ann Arbor, MI, USA
Milind Prabhu
  • University of Michigan, Ann Arbor, MI, USA

Funding

  • Bansal, Nikhil: Supported in part by the NWO VICI grant 639.023.812.

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