Tight lower bounds on envy-free makespan approximation

  • Authors:

  • Amos Fiat;Ariel Levavi

  • Affiliations:

  • School of Computer Science, Tel Aviv University, Tel Aviv, Israel;School of Computer Science and Engineering, UC San Diego, San Diego, CA

  • Venue:
  • WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
  • Year:
  • 2012

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Abstract

In this work we give a tight lower bound on makespan approximation for envy-free allocation mechanisms dedicated to scheduling tasks on unrelated machines. Specifically, we show that no mechanism exists that can guarantee an envy-free allocation of jobs to m machines with a makespan less than a factor of O(logm) of the minimal makespan. Combined with previous results, this paper definitively proves that the optimal algorithm for obtaining a minimal makespan for any envy-free division can at best approximate the makespan to a factor of O(logm).