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
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Constant-Factor Approximation Algorithm for the Multicommodity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
An Edge in Time Saves Nine: LP Rounding Approximation Algorithms for Stochastic Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems
Mathematical Programming: Series A and B
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Sharing the cost more efficiently: Improved approximation for multicommodity rent-or-buy
ACM Transactions on Algorithms (TALG)
Approximating connected facility location problems via random facility sampling and core detouring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic Sampling Algorithms for Network Design
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A constant-factor approximation for stochastic Steiner forest
Proceedings of the forty-first annual ACM symposium on Theory of computing
Pricing tree access networks with connected backbones
ESA'07 Proceedings of the 15th annual European conference on Algorithms
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Stochastic steiner trees without a root
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A simpler and better derandomization of an approximation algorithm for single source rent-or-buy
Operations Research Letters
Sampling and Cost-Sharing: Approximation Algorithms for Stochastic Optimization Problems
SIAM Journal on Computing
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Gupta et al. [J. ACM, 54 (2007), article 11] and Gupta, Kumar, and Roughgarden [in Proceedings of the ACM Symposium on Theory of Computing, ACM, New York, 2003, pp. 365-372] recently developed an elegant framework for the development of randomized approximation algorithms for rent-or-buy network design problems. The essential building block of this framework is an approximation algorithm for the underlying network design problem that admits a strict cost sharing scheme. Such cost sharing schemes have also proven to be useful in the development of approximation algorithms in the context of two-stage stochastic optimization with recourse. The main contribution of this paper is to show that the Steiner forest problem admits cost shares that are 3-strict and 4-group-strict. As a consequence, we derive surprisingly simple approximation algorithms for the multicommodity rent-or-buy and the multicast rent-or-buy problems with approximation ratios 5 and 6, improving over the previous best approximation ratios of 6.828 and 12.8, respectively. We also show that no approximation ratio better than 4.67 can be achieved using the sample-and-augment framework in combination with the currently best known Steiner forest approximation algorithms. In the context of two-stage stochastic optimization, our result leads to a 6-approximation algorithm for the stochastic Steiner tree problem in the black-box model and a 5-approximation algorithm for the stochastic Steiner forest problem in the independent decision model.