A Group-Strategyproof Cost Sharing Mechanism for the Steiner Forest Game

Jochen Könemann, Stefano Leonardi, Guido Schäfer, Stefan H. M. van Zwam
2008 SIAM journal on computing (Print)  
We consider a game-theoretical variant of the Steiner forest problem in which each player j, out of a set of k players, strives to connect his terminal pair (s j , t j ) of vertices in an undirected, edge-weighted graph G. In this paper we show that a natural adaptation of the primaldual Steiner forest algorithm of Agrawal, Klein, and Ravi [SIAM J. Comput., 24 (1995), pp. 445-456] yields a 2-budget balanced and cross-monotonic cost sharing method for this game. We also present a negative
more » ... arguing that no cross-monotonic cost sharing method can achieve a budget balance factor of less than 2 for the Steiner tree game. This shows that our result is tight. Our algorithm gives rise to a new linear programming relaxation for the Steiner forest problem which we term the lifted-cut relaxation. We show that this new relaxation is stronger than the standard undirected cut relaxation for the Steiner forest problem.
doi:10.1137/050646408 fatcat:qzuk6znt55gqxdix4g5awovxjq