Cost-Sharing Mechanisms for Network Design

We consider a single source network design problem from a game-theoretic perspective. Gupta, Kumar and Roughgarden (Proc. 35th Annual ACM STOC, pages 365-372, 2003) developed a simple method for single source rent-or-buy problem that also yields the best-known approximation ratio for the problem. We show how to use a variant of this method to develop an approximately budget-balanced and group strategyproof cost-sharing method for the problem. The novelty of our approach stems from our obtaining the cost-sharing methods for the rent-or-buy problem by carefully combining cost-shares for the simpler problem Steiner tree problem; we feel that this idea may have wider implications. Our algorithm is conceptually simpler than the previous such cost-sharing method due to Pal and Tardos (Proc. 44th Annual FOCS, pages 584-593, 2003), and has a much improved approximation factor of 4.6 (over the previously known factor of 15).

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

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

[3]  Alex Zelikovsky,et al.  Improved Steiner tree approximation in graphs , 2000, SODA '00.

[4]  Aravind Srinivasan,et al.  Chernoff-Hoeffding bounds for applications with limited independence , 1995, SODA '93.

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

[6]  Mihir Bellare,et al.  Randomness-efficient oblivious sampling , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

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

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

[9]  Amit Kumar,et al.  Provisioning a virtual private network: a network design problem for multicommodity flow , 2001, STOC '01.

[10]  Michael Luby.  A Simple Parallel Algorithm for the Maximal Independent Set Problem , 1986, SIAM J. Comput..

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

[12]  William W. Sharkey,et al.  Cost allocation , 1996 .

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