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
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
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
Sharing the cost more efficiently: improved approximation for multicommodity rent-or-buy
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Stochastic steiner trees without a root
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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)
Stochastic analyses for online combinatorial optimization problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating connected facility location problems via random facility sampling and core detouring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal Efficiency Guarantees for Network Design Mechanisms
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A constant-factor approximation for stochastic Steiner forest
Proceedings of the forty-first annual ACM symposium on Theory of computing
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
Steiner forests on stochastic metric graphs
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Connected facility location via random facility sampling and core detouring
Journal of Computer and System Sciences
Network design via core detouring for problems without a core
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Designing Network Protocols for Good Equilibria
SIAM Journal on Computing
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk
Mathematics of Operations Research
Approximation algorithms for single and multi-commodity connected facility location
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
A simpler and better derandomization of an approximation algorithm for single source rent-or-buy
Operations Research Letters
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In the multi-commodity rent-or-buy network design problem (MRoB) we are given a network together with a set of k terminal pairs R = (s_1, t_1), ..., (s_k, t_k). The goal is to install capacities on the edges of the network so that a prescribed amount of flow fi can be routed between all terminal pairs si and ti simultaneously. We can either rent capacity on an edge at some cost per unit flow or buy infinite capacity on an edge at some larger fixed cost. The overall objective is to install capacities at a minimum total cost.The version of the stochastic Steiner tree problem (SST) considered here is the Steiner tree problem in the model of two-stage stochastic optimization with recourse. In stage one, there is a known probability distribution on subsets of vertices and we can choose to buy a subset of edges at a given cost. In stage two, a subset of vertices T from the prior known distribution is realized, and additional edges can be bought at a possibly higher cost. The objective is to buy a set of edges in stages one and two so that all vertices in T are connected, and the expected cost is minimized.Gupta et al. (FOCS '03) give a randomized scheme for the MRoB problem that was both used subsequently to improve the approximation ratio for this problem, and extended to yield the best approximation algorithm for SST. One building block of this scheme is a good approximation algorithm for Steiner forests.We present a surprisingly simple 5-approximation algorithm for MRoB and 6-approximation for SST, improving on the best previous guarantees of 6.828 and 12.6, and show that no approximation ratio better than 4.67 can be achieved using the above mentioned randomized scheme in combination with the currently best known Steiner forest approximation algorithms. A key component of our approach are cost shares that are 3-strict for the unmodified primal-dual Steiner forest algorithm.