Adjustable robust solutions of uncertain linear programs
Mathematical Programming: Series A and B
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
Robust Combinatorial Optimization with Exponential Scenarios
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Two-Stage Robust Network Design with Exponential Scenarios
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Thresholded covering algorithms for robust and max-min optimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Theory and Applications of Robust Optimization
SIAM Review
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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
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We consider a class of multi-stage robust covering problems, where additional information is revealed about the problem instance in each stage, but the cost of taking actions increases. The dilemma for the decision-maker is whether to wait for additional information and risk the inflation, or to take early actions to hedge against rising costs. We study the "k-robust" uncertainty model: in each stage i=0, 1, …, T, the algorithm is shown some subset of size ki that completely contains the eventual demands to be covered; here k1k2⋯kT which ensures increasing information over time. The goal is to minimize the cost incurred in the worst-case possible sequence of revelations. For the multistage k-robust set cover problem, we give an O(logm+logn)-approximation algorithm, nearly matching the $\Omega\left(\log n+\frac{\log m}{\log\log m}\right)$ hardness of approximation [4] even for T=2 stages. Moreover, our algorithm has a useful "thrifty" property: it takes actions on just two stages. We show similar thrifty algorithms for multi-stage k-robust Steiner tree, Steiner forest, and minimum-cut. For these problems our approximation guarantees are O( min { T, logn, logλmax }), where λmax is the maximum inflation over all the stages. We conjecture that these problems also admit O(1)-approximate thrifty algorithms.