Cost Sharing Methods for Makespan and Completion Time Scheduling

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 Ω(logn) 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.