Abstract
Könemann, Leonardi, and Schäfer [14] gave a 2-budget-balanced and groupstrategyproof mechanism for Steiner forest cost-sharing problems. We prove that this mechanism also achieves an O(log2 k)-approximation of the social cost, where k is the number of players. As a consequence, the KLS mechanism has the smallest-possible worst-case efficiency loss, up to constant factors, among all O(1)-budget-balanced Moulin mechanisms for such cost functions. We also extend our results to a more general network design problem.
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References
Agrawal, A., Klein, P., Ravi, R.: When trees collide: an approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing 24(3), 440–456 (1995)
Archer, A., Feigenbaum, J., Krishnamurthy, A., Sami, R., Shenker, S.: Approximation and collusion in multicast cost sharing. Games and Economic Behavior 47(1), 36–71 (2004)
Bartal, Y.: Probabilistic approximations of metric spaces and its algorithmic applications. In: Proceedings of the 37th Annual Symposium on Foundations of Computer Science (FOCS), pp. 184–193 (1996)
Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. In: Proceedings of the 35th Annual ACM Symposium on the Theory of Computing (STOC) (2003)
Feigenbaum, J., Krishnamurthy, A., Sami, R., Shenker, S.: Hardness results for multicast cost sharing. Theoretical Computer Science 304, 215–236 (2003)
Feigenbaum, J., Papadimitriou, C., Shenker, S.: Sharing the cost of multicast transmissions. Journal of Computer and System Sciences 63(1), 21–41 (2001)
Goemans, M.X., Williamson, D.P.: A general approximation technique for constrained forest problems. SIAM Journal on Computing 24(2), 296–317 (1995)
Green, J., Kohlberg, E., Laffont, J.J.: Partial equilibrium approach to the free rider problem. Journal of Public Economics 6, 375–394 (1976)
Gupta, A., Srinivasan, A., Tardos, É.: Cost-sharing mechanisms for network design. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, pp. 139–150. Springer, Heidelberg (2004)
Immorlica, N., Mahdian, M., Mirrokni, V.S.: Limitations of cross-monotonic cost-sharing schemes. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 602–611 (2005)
Jain, K., Vazirani, V.: Applications of approximation algorithms to cooperative games. In: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing (STOC), pp. 364–372 (2001)
Jain, K., Vazirani, V.: Equitable cost allocations via primal-dual-type algorithms. In: Proceedings of the 34th Annual ACM Symposium on the Theory of Computing (STOC), pp. 313–321 (2002)
Kent, K., Skorin-Kapov, D.: Population monotonic cost allocation on mst’s. In: Operational Research Proceedings KOI, pp. 43–48 (1996)
Könemann, J., Leonardi, S., Schäfer, G.: A group-strategyproof mechanism for Steiner forests. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 612–619 (2005)
Könemann, J., Leonardi, S., Schäfer, G., van Zwam, S.: From primal-dual to cost shares and back: A stronger LP relaxation for the steiner forest problem. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1051–1063. Springer, Heidelberg (2005)
Leonardi, S., Schäfer, G.: Cross-monotonic cost-sharing methods for connected facility location. In: Proceedings of the Fifth ACM Conference on Electronic Commerce (EC), pp. 242–243 (2004)
Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, Oxford (1995)
Moulin, H.: Incremental cost sharing: Characterization by coalition strategy-proofness. Social Choice and Welfare 16, 279–320 (1999)
Moulin, H., Shenker, S.: Strategyproof sharing of submodular costs: Budget balance versus efficiency. Economic Theory 18, 511–533 (2001)
Pál, M., Tardos, É.: Group strategyproof mechanisms via primal-dual algorithms. In: Proceedings of the 44th Annual Symposium on Foundations of Computer Science (FOCS), pp. 584–593 (2003)
Roberts, K.: The characterization of implementable choice rules. In: Laffont, J.J. (ed.) Aggregation and Revelation of Preferences. North-Holland, Amsterdam (1979)
Roughgarden, T., Sundararajan, M.: Approximately efficient cost-sharing mechanisms (submitted, 2006)
Roughgarden, T., Sundararajan, M.: New trade-offs in cost-sharing mechanisms. In: Proceedings of the 38th Annual ACM Symposium on the Theory of Computing (STOC), pp. 79–88 (2006)
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Chawla, S., Roughgarden, T., Sundararajan, M. (2006). Optimal Cost-Sharing Mechanisms for Steiner Forest Problems. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds) Internet and Network Economics. WINE 2006. Lecture Notes in Computer Science, vol 4286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944874_11
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DOI: https://doi.org/10.1007/11944874_11
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