A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
A deterministic algorithm for the cost-distance problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual 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
Online algorithms for network design
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
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
Stochastic Optimization is (Almost) as easy as Deterministic Optimization
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On non-uniform multicommodity buy-at-bulk network design
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Network design for information networks
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the approximability of some network design problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
Sampling-based Approximation Algorithms for Multi-stage Stochastic
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Stochastic steiner trees without a root
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On two-stage stochastic minimum spanning trees
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
What about wednesday? approximation algorithms for multistage stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Sampling bounds for stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Matching based augmentations for approximating connectivity problems
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
New results on the complexity of the max- and min-rep problems
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
A note on the subadditive network design problem
Operations Research Letters
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We study the Steiner Tree problem in the model of two-stage stochastic optimization with non-uniform inflation factors, and give a poly-logarithmic approximation factor for this problem. In this problem, we are given a graph G= (V,E), with each edge having two costs cMand cT(the costs for Monday and Tuesday, respectively). We are also given a probability distribution 茂戮驴: 2V茂戮驴[0,1] over subsets of V, and will be given a client setSdrawn from this distribution on Tuesday. The algorithm has to buy a set of edges EMon Monday, and after the client set Sis revealed on Tuesday, it has to buy a (possibly empty) set of edges ET(S) so that the edges in EM茂戮驴 ET(S) connect all the nodes in S. The goal is to minimize the cM(EM) + ES茂戮驴茂戮驴[ cT( ET(S) ) ].We give the first poly-logarithmic approximation algorithm for this problem. Our algorithm builds on the recent techniques developed by Chekuri et al. (FOCS 2006) for multi-commodity Cost-Distance. Previously, the problem had been studied for the cases when cT= 茂戮驴×cMfor some constant 茂戮驴茂戮驴 1 (i.e., the uniformcase), or for the case when the goal was to find a tree spanning all the verticesbut Tuesday's costs were drawn from a given distribution $\widehat{\pi}$ (the so-called "stochastic MST case").We complement our results by showing that our problem is at least as hard as the single-sink Cost-Distance problem (which is known to be 茂戮驴(loglogn) hard). Moreover, the requirement that Tuesday's costs are fixed seems essential: if we allow Tuesday's costs to dependent on the scenario as in stochastic MST, the problem becomes as hard as Label Cover (which is $\Omega(2^{\log^{1-\varepsilon} n})$-hard). As an aside, we also give an LP-rounding algorithm for the multi-commodity Cost-Distance problem, matching the O(log4n) approximation guarantee given by Chekuri et al. (FOCS 2006).