Singleton acyclic mechanisms and their applications to scheduling problems

Abstract

Mehta, Roughgarden, and Sundararajan recently introduced a new class of cost sharing mechanisms called acyclic mechanisms. These mechanisms achieve a slightly weaker notion of truthfulness than the well-known Moulin mechanisms, but provide additional freedom to improve budget balance and social cost approximation guarantees. In this paper, we investigate the potential of acyclic mechanisms for combinatorial optimization problems. In particular, we study a subclass of acyclic mechanisms which we term singleton acyclic mechanisms. We show that every ρ-approximate algorithm that is partially increasing can be turned into a singleton acyclic mechanism that is weakly group-strategyproof and ρ-budget balanced. Based on this result, we develop singleton acyclic mechanisms for parallel machine scheduling problems with completion time objectives, which perform extremely well both with respect to budget balance and social cost. © 2008 Springer-Verlag Berlin Heidelberg.