Group strategy proof mechanisms via primal-dual algorithms

We develop a general method for turning a primal-dual algorithm into a group strategy proof cost-sharing mechanism. We use our method to design approximately budget balanced cost sharing mechanisms for two NP-complete problems: metric facility location, and single source rent-or-buy network design. Both mechanisms are competitive, group strategyproof and recover a constant fraction of the cost. For the facility location game our cost-sharing method recovers a 1/3rd of the total cost, while in the network design game the cost shares pay for a 1/15 fraction of the cost of the solution.

[1]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[2]  Tim Roughgarden,et al.  Simpler and better approximation algorithms for network design , 2003, STOC '03.

[3]  Nikhil R. Devanur,et al.  Strategyproof cost-sharing mechanisms for set cover and facility location games , 2003, EC '03.

[4]  C. Greg Plaxton,et al.  The online median problem , 1999, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[5]  Vijay V. Vazirani,et al.  Equitable cost allocations via primal-dual-type algorithms , 2002, STOC '02.

[6]  David B. Shmoys,et al.  Lagrangian Relaxation for the k-Median Problem: New Insights and Continuity Properties , 2003, ESA.

[7]  Sudipto Guha,et al.  A constant factor approximation for the single sink edge installation problems , 2001, STOC '01.

[8]  Vijay V. Vazirani,et al.  Primal-dual approximation algorithms for metric facility location and k-median problems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[9]  R. Ravi,et al.  When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks , 1995, SIAM J. Comput..

[10]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[11]  Mohammad Mahdian,et al.  Improved Approximation Algorithms for Metric Facility Location Problems , 2002, APPROX.

[12]  Sanjeev Goyal,et al.  A Noncooperative Model of Network Formation , 2000 .

[13]  Sándor P. Fekete,et al.  On approximately fair cost allocation in Euclidean TSP games , 1998, Electron. Colloquium Comput. Complex..

[14]  R. Ravi,et al.  Approximation Algorithms for the Traveling Purchaser Problem and its Variants in Network Design , 1999, ESA.

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

[16]  H. Moulin.  Cooperative Microeconomics: A Game-Theoretic Introduction , 1995 .

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

[18]  Nikhil R. Devanur,et al.  Market equilibrium via a primal-dual-type algorithm , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[19]  David R. Karger,et al.  Building Steiner trees with incomplete global knowledge , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[20]  Tim Roughgarden,et al.  A constant-factor approximation algorithm for the multicommodity rent-or-buy problem , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[21]  R. Ravi,et al.  On the Integrality Gap of a Natural Formulation of the Single-Sink Buy-at-Bulk Network Design Problem , 2001, IPCO.

[22]  Hans Haller,et al.  Nash Networks with Heterogeneous Agents , 2000 .

[23]  Chaitanya Swamy,et al.  Primal-Dual Algorithms for Connected Facility Location Problems , 2002, APPROX.

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

[25]  Scott Shenker,et al.  On a network creation game , 2003, PODC '03.

[26]  Sudipto Guha,et al.  Hierarchical placement and network design problems , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[27]  Martin Skutella,et al.  Cooperative facility location games , 2000, SODA '00.

[28]  van Shm Stefan Zwam,et al.  Cost sharing mechanisms for network games , 2005 .

[29]  Éva Tardos,et al.  Near-optimal network design with selfish agents , 2003, STOC '03.

[30]  David P. Williamson,et al.  A general approximation technique for constrained forest problems , 1992, SODA '92.

[31]  Joan Feigenbaum,et al.  Sharing the cost of muliticast transmissions (preliminary version) , 2000, STOC '00.