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(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.

[1]  Tim Roughgarden,et al.  New trade-offs in cost-sharing mechanisms , 2006, STOC '06.

[2]  Vijay V. Vazirani,et al.  Applications of approximation algorithms to cooperative games , 2001, STOC '01.

[3]  Joan Feigenbaum,et al.  Hardness Results for Multicast Cost Sharing , 2002, FSTTCS.

[4]  Ron Lavi,et al.  Algorithmic Mechanism Design , 2008, Encyclopedia of Algorithms.

[5]  Nicole Immorlica,et al.  Limitations of cross-monotonic cost sharing schemes , 2005, SODA '05.

[6]  Tim Roughgarden,et al.  Optimal Cost-Sharing Mechanisms for Steiner Forest Problems , 2006, WINE.

[7]  Jerry R. Green,et al.  Partial Equilibrium Approach to the Free-Rider Problem , 1976 .

[8]  Dorit S. Hochba,et al.  Approximation Algorithms for NP-Hard Problems , 1997, SIGA.

[9]  H. Moulin,et al.  Strategyproof sharing of submodular costs:budget balance versus efficiency , 2001 .

[10]  Joan Feigenbaum,et al.  Sharing the Cost of Multicast Transmissions , 2001, J. Comput. Syst. Sci..

[11]  Jochen Könemann,et al.  A group-strategyproof mechanism for Steiner forests , 2005, SODA '05.

[12]  Ryan Porter,et al.  Mechanism design for online real-time scheduling , 2004, EC '04.

[13]  J. Laffont.  Aggregation and revelation of preferences , 1979 .

[14]  Stefano Leonardi,et al.  Cross-monotonic cost-sharing methods for connected facility location games , 2004, EC '04.

[15]  Tim Roughgarden,et al.  Approximately Efficient Cost-Sharing Mechanisms , 2006, ArXiv.

[16]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[17]  Joan Feigenbaum,et al.  Approximation and collusion in multicast cost sharing , 2003, EC '03.

[18]  Stefano Leonardi,et al.  Algorithms - ESA 2005, 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005, Proceedings , 2005, ESA.

[19]  Rudolf Müller,et al.  Decentralization and Mechanism Design for Online Machine Scheduling , 2006, SWAT.

[20]  Annamária Kovács,et al.  Fast Monotone 3-Approximation Algorithm for Scheduling Related Machines , 2005, ESA.

[21]  Jochen Könemann,et al.  From Primal-Dual to Cost Shares and Back: A Stronger LP Relaxation for the Steiner Forest Problem , 2005, ICALP.

[22]  Aravind Srinivasan,et al.  Cost-Sharing Mechanisms for Network Design , 2004, APPROX-RANDOM.

[23]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[24]  Stefano Leonardi,et al.  Cross-monotonic cost sharing methods for connected facility location games , 2004, Theor. Comput. Sci..

[25]  R. Ravi,et al.  An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem , 2007, SODA '07.

[26]  Burkhard Monien,et al.  Fair cost-sharing methods for scheduling jobs on parallel machines , 2009, J. Discrete Algorithms.

[27]  Éva Tardos,et al.  Group strategy proof mechanisms via primal-dual algorithms , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..