Stefan H. M. van Zwam

Jochen Könemann; Stefano Leonardi; Guido Schäfer; Stefan H. M. van Zwam

We consider a game-theoretical variant of the Steiner forest problem, in which each of k users i strives to connect his terminal pair (si, ti) of vertices in an undirected, edge-weighted graph G. In [1] a natural primal-dual algorithm was shown which achieved a 2-approximate budget balanced cross-monotonic cost sharing method for this game. We derive a new linear programming relaxation from the techniques of [1] which allows for a simpler proof of the budget balancedness of the algorithm from [1]. Furthermore we show that this new relaxation is strictly stronger than the well-known undirected cut relaxation for the Steiner forest problem. We conclude the paper with a negative result, arguing that no cross-monotonic cost sharing method can achieve a budget balance factor of less than 2 for the Steiner tree and Steiner forest games. This shows that the results of [1,2] are essentially tight.

Jochen Könemann; Stefano Leonardi; Guido Schäfer; Stefan H. M. van Zwam

We consider a game-theoretical variant of the Steiner forest problem in which each player

Dillon Mayhew; Geoff Whittle; Stefan H. M. van Zwam

j

Dillon Mayhew; Geoff Whittle; Stefan H. M. van Zwam

, out of a set of

Peter Nelson; Stefan H. M. van Zwam

k

Kevin Grace; Stefan H. M. van Zwam

players, strives to connect his terminal pair

Jim Geelen; Stefan H. M. van Zwam

(s_j, t_j)

Peter Nelson; Stefan H. M. van Zwam

of vertices in an undirected, edge-weighted graph

Peter Nelson; Stefan H. M. van Zwam

G

Kevin Grace; Stefan H. M. van Zwam

. In this paper we show that a natural adaptation of the primal-dual Steiner forest algorithm of Agrawal, Klein, and Ravi [SIAM J. Comput., 24 (1995), pp. 445-456] yields a