Tight Lower Bounds on Envy-Free Makespan Approximation
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).
Keywordsmakespan approximation locally-efficient envy-freeness mechanism design scheduling
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