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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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Journal of the ACM (JACM)
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An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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ESA'07 Proceedings of the 15th annual European conference on Algorithms
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WINE'06 Proceedings of the Second international conference on Internet and Network Economics
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ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Fair cost-sharing methods for scheduling jobs on parallel machines
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
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MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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In this paper we design an approximately budget-balanced and group-strategyproof cost-sharing mechanism for the Steiner forest game. An instance of this game consists of an undirected graph G = (V, E), non-negative costs ce for all edges e ∈ E, and a set R ⊆ V x V of k terminal pairs. Each terminal pair (s, t) ∈ R is associated with an agent that wishes to establish a connection between nodes s and t in the underlying network. A feasible solution is a forest F that contains an s, t-path for each connection request (s, t) ∈ R.Previously, Jain and Vazirani [4] gave a 2-approximate budget-balanced and group-strategyproof cost-sharing mechanism for the Steiner tree game --- a special case of the game considered here. Such a result for Steiner forest games has proved to be elusive so far, in stark contrast to the well known primal-dual (2 -- 1/k)-approximate algorithms [1, 2] for the problem.The cost-sharing method presented in this paper is 2-approximate budget-balanced and this is tight with respect to the budget-balance factor.Our algorithm is an original extension of known primal-dual methods for Steiner forests [1]. An interesting byproduct of the work in this paper is that our Steiner forest algorithm is (2 -- 1/k)-approximate despite the fact that the forest computed by our method is usually costlier than those computed by known primal-dual algorithms. In fact the dual solution computed by our algorithm is infeasible but we can still prove that its total value is at most the cost of a minimum-cost Steiner forest for the given instance.