TY - GEN

T1 - An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem

AU - Gupta, A.

AU - Könemann, J.

AU - Leonardi, S.

AU - Ravi, R.

AU - Schäfer, G.

N1 - Publisher Copyright:
Copyright © 2007 by the Association for Computing Machinery, Inc. and the Society for Industrial and Applied Mathematics.

PY - 2007

Y1 - 2007

N2 - In an instance of the prize-collecting Steiner forest problem (PCSF) we are given an undirected graph G = (V,E), non-negative edge-costs c(e) for all e ∈ E, terminal pairs R = {(si, ti)}1≤i≤k, and penalties π1, ⋯, π k. A feasible solution (F,Q) consists of a forest F and a subset Q of terminal pairs such that for all (si, ti) ∈ R either si, ti are connected by F or (si, ti) ∈ Q. The objective is to compute a feasible solution of minimum cost c(F) + π(Q). A game-theoretic version of the above problem has k players, one for each terminal-pair in R. Player i's ultimate goal is to connect si and ti, and the player derives a privately held utility ui ≥ 0 from being connected. A service provider can connect the terminals si and ti of player i in two ways: (1) by buying the edges of an si, ti-path in G, or (2) by buying an alternate connection between si and ti (maybe from some other provider) at a cost of πi. In this paper, we present a simple 3-budget-balanced and group-strategyproof mechanism for the above problem. We also show that our mechanism computes client sets whose social cost is at most O(log2 k) times the minimum social cost of any player set. This matches a lower-bound that was recently given by Roughgarden and Sundararajan (STOC '06).

AB - In an instance of the prize-collecting Steiner forest problem (PCSF) we are given an undirected graph G = (V,E), non-negative edge-costs c(e) for all e ∈ E, terminal pairs R = {(si, ti)}1≤i≤k, and penalties π1, ⋯, π k. A feasible solution (F,Q) consists of a forest F and a subset Q of terminal pairs such that for all (si, ti) ∈ R either si, ti are connected by F or (si, ti) ∈ Q. The objective is to compute a feasible solution of minimum cost c(F) + π(Q). A game-theoretic version of the above problem has k players, one for each terminal-pair in R. Player i's ultimate goal is to connect si and ti, and the player derives a privately held utility ui ≥ 0 from being connected. A service provider can connect the terminals si and ti of player i in two ways: (1) by buying the edges of an si, ti-path in G, or (2) by buying an alternate connection between si and ti (maybe from some other provider) at a cost of πi. In this paper, we present a simple 3-budget-balanced and group-strategyproof mechanism for the above problem. We also show that our mechanism computes client sets whose social cost is at most O(log2 k) times the minimum social cost of any player set. This matches a lower-bound that was recently given by Roughgarden and Sundararajan (STOC '06).

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M3 - Conference contribution

AN - SCOPUS:84969172410

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1153

EP - 1162

BT - Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007

PB - Association for Computing Machinery

T2 - 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007

Y2 - 7 January 2007 through 9 January 2007

ER -