Fair Cost-Sharing Methods for Scheduling Jobs on Parallel Machines

  • Yvonne Bleischwitz
  • Burkhard Monien
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


We consider the problem of sharing the cost of scheduling n jobs on m parallel machines among a set of agents. In our setting, each agent owns one job and the cost is given by the makespan of the computed assignment. We focus on α-budget-balanced cross-monotonic cost-sharing methods since they guarantee the two substantial mechanism properties α-budget-balance and group-strategyproofness and provide fair cost-shares. For identical jobs on related machines and for arbitrary jobs on identical machines, we give (m+1)/(2m)-budget-balanced cross-monotonic cost-sharing methods and show that this is the best approximation possible. As our major result, we prove that the approximation factor for cross-monotonic cost-sharing methods is unbounded for arbitrary jobs and related machines. We therefore develop a cost-sharing method in the (m+1)/(2m)-core, a weaker but also fair solution concept. We close with a strategyproof mechanism for the model of arbitrary jobs and related machines that recovers at least 3/5 of the cost. All given solutions can be computed in polynomial time.


Nash Equilibrium Schedule Problem Completion Time Parallel Machine Steiner Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yvonne Bleischwitz
    • 1
    • 2
  • Burkhard Monien
    • 1
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.International Graduate School of Dynamic Intelligent Systems 

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