The cost of selfishness for maximizing the minimum load on uniformly related machines

Leah Epstein, Elena Kleiman, Rob Van Stee

Research output: Contribution to journalArticlepeer-review


Consider the following scheduling game. A set of jobs, each controlled by a selfish agent, are to be assigned to m uniformly related machines. The cost of a job is defined as the total load of the machine that its job is assigned to. A job is interested in minimizing its cost, while the social objective is maximizing the minimum load (the value of the cover) over the machines. This goal is different from the regular makespan minimization goal, which was extensively studied in a game theoretic context. We study the price of anarchy (poa) and the price of stability (pos) for uniformly related machines. The results are expressed in terms of s, which is the maximum speed ratio between any two machines. For uniformly related machines, we prove that the pos is unbounded for s>2, and the poa is unbounded for s≥2. For the remaining cases we show that while the poa grows to infinity as s tends to 2, the pos is at most 2 for any s≤2.

Original languageEnglish
Pages (from-to)767-777
Number of pages11
JournalJournal of Combinatorial Optimization
Issue number4
StatePublished - May 2014


  • Machine scheduling
  • Maximizing the minimum load
  • Price of anarchy
  • Price of stability

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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