91A12 Cooperative games
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 rho-approximate algorithm that is partially increasing can be turned into a singleton acyclic mechanism that is weakly group-strategyproof and rho-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.
Roughgarden and Sundararajan recently introduced an alternative measure
of efficiency for cost sharing mechanisms.
We study cost sharing methods for combinatorial optimization problems
using this novel efficiency measure, with a particular focus on
scheduling problems. While we prove a lower bound of $\Omega(\log n)$ for a very general class of problems, we give a best possible cost sharing method for minimum makespan scheduling. Finally, we show that no budget balanced cost sharing methods for completion or flow time objectives exist.