A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Median bounds and their application
Journal of Algorithms
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A general approach to online network optimization problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Operations Research
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Adjustable robust solutions of uncertain linear programs
Mathematical Programming: Series A and B
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
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
SIAM Journal on Computing
How to Pay, Come What May: Approximation Algorithms for Demand-Robust Covering Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
A plant location guide for the unsure
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Permutation betting markets: singleton betting with extra information
Proceedings of the 9th ACM conference on Electronic commerce
Approximating Single Machine Scheduling with Scenarios
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Two-Stage Robust Network Design with Exponential Scenarios
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems
Mathematics of Operations Research
Thresholded covering algorithms for robust and max-min optimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
An s-t connection problem with adaptability
Discrete Applied Mathematics
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Optimization over integers with robustness in cost and few constraints
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Single machine scheduling with scenarios
Theoretical Computer Science
Thrifty algorithms for multistage robust optimization
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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Following the well-studied two-stage optimization framework for stochastic optimization [15,8], we study approximation algorithms for robust two-stage optimization problems with an exponential number of scenarios. Prior to this work, Dhamdhere et al. [8] introduced approximation algorithms for two-stage robust optimization problems with explicitly given scenarios. In this paper, we assume the set of possible scenarios is given implicitly, for example by an upper bound on the number of active clients. In two-stage robust optimization, we need to pre-purchase some resources in the first stage before the adversary's action. In the second stage, after the adversary chooses the clients that need to be covered, we need to complement our solution by purchasing additional resources at an inflated price. The goal is to minimize the cost in the worst-case scenario. We give a general approach for solving such problems using LP rounding. Our approach uncovers an interesting connection between robust optimization and online competitive algorithms. We use this approach, together with known online algorithms, to develop approximation algorithms for several robust covering problems, such as set cover, vertex cover, and edge cover. We also study a simple buy-at-oncealgorithm that either covers all items in the first stage or does nothing in the first stage and waits to build the complete solution in the second stage. We show that this algorithm gives tight approximation factors for unweighted variants of these covering problems, but performs poorly for general weighted problems.