The steiner problem with edge lengths 1 and 2,
Information Processing Letters
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Limitations of cross-monotonic cost sharing schemes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A group-strategyproof mechanism for Steiner forests
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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
Limitations of cross-monotonic cost-sharing schemes
ACM Transactions on Algorithms (TALG)
Group-strategyproof cost sharing mechanisms for makespan and other scheduling problems
Theoretical Computer Science
Singleton Acyclic Mechanisms and Their Applications to Scheduling Problems
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Fair cost-sharing methods for scheduling jobs on parallel machines
Journal of Discrete Algorithms
Cost sharing methods for makespan and completion time scheduling
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Pricing tree access networks with connected backbones
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Optimal cost-sharing mechanisms for steiner forest problems
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Fair cost-sharing methods for scheduling jobs on parallel machines
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
The power of two prices: beyond cross-monotonicity
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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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.