On Minimizing Generalized Makespan on Unrelated Machines

Authors Nikhil Ayyadevara, Nikhil Bansal, Milind Prabhu

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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

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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)


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.

Subject Classification

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


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