Stefan H. M. van Zwam

From primal-dual to cost shares and back: a stronger LP relaxation for the steiner forest problem

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.

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

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

Stability, fragility, and Rota's Conjecture

j

An Obstacle to a Decomposition Theorem for Near-Regular Matroids

, out of a set of

On the Existence of Asymptotically Good Linear Codes in Minor-Closed Classes

k

Templates for Binary Matroids

players, strives to connect his terminal pair

Matroid 3-connectivity and branch width

(s_j, t_j)

The Maximum-Likelihood Decoding Threshold for Cycle Codes of Graphs

of vertices in an undirected, edge-weighted graph

Matroids Representable Over Fields With a Common Subfield

G

On Perturbations of Highly Connected Dyadic Matroids

. 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