Maximizing the minimum load: The cost of selfishness

Leah Epstein, Elena Kleiman, Rob Van Stee

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider a scheduling problem where each job is controlled by a selfish agent, who is only interested in minimizing its own cost, which is defined as the total load on the machine that its job is assigned to. We consider the objective of maximizing the minimum load (cover) over the machines. Unlike the regular makespan minimization problem, which was extensively studied in a game theoretic context, this problem has not been considered in this setting before. We study the price of anarchy (poa) and the price of stability (pos). We show that on related machines, both these values are unbounded. We then focus on identical machines. We show that the is 1, and we derive tight bounds on the for m≤6 and nearly tight bounds for general m. In particular, we show that the is at least 1.691 for larger m and at most 1.7. Hence, surprisingly, the is less than the for the makespan problem, which is 2. To achieve the upper bound of 1.7, we make an unusual use of weighting functions. Finally, in contrast we show that the mixed grows exponentially with m for this problem, although it is only Θ(logm/loglogm) for the makespan.

Original languageEnglish
Title of host publicationInternet and Network Economics - 5th International Workshop, WINE 2009, Proceedings
Number of pages12
StatePublished - 2009
Event5th International Workshop on Internet and Network Economics, WINE 2009 - Rome, Italy
Duration: 14 Dec 200918 Dec 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5929 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference5th International Workshop on Internet and Network Economics, WINE 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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