A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Approximation algorithms for Steiner and directed multicuts
Journal of Algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh 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
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
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
On two-stage stochastic minimum spanning trees
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for requirement cut on graphs
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
A plant location guide for the unsure
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
A Plant Location Guide for the Unsure: Approximation Algorithms for Min-Max Location 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
On the approximability of robust spanning tree problems
Theoretical Computer Science
An s-t connection problem with adaptability
Discrete Applied Mathematics
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Thrifty algorithms for multistage robust optimization
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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Demand-robust versions of common optimization problems were recently introduced by Dhamdhere et al. [4] motivated by the worst-case considerations of two-stage stochastic optimization models. We study the demand robust min-cut and shortest path problems, and exploit the nature of the robust objective to give improved approximation factors. Specifically, we give a $(1 + \sqrt{2})$ approximation for robust min-cut and a 7.1 approximation for robust shortest path. Previously, the best approximation factors were O(log n) for robust min-cut and 16 for robust shortest paths, both due to Dhamdhere et al.[4]. Our main technique can be summarized as follows: We investigate each of the second stage scenarios individually, checking if it can be independently serviced in the second stage within an acceptable cost (namely, a guess of the optimal second stage costs). For the costly scenarios that cannot be serviced in this way (“rainy days”), we show that they can be fully taken care of in a near-optimal first stage solution (i.e., by ”paying today”). We also consider “hitting-set” extensions of the robust min-cut and shortest path problems and show that our techniques can be combined with algorithms for Steiner multicut and group Steiner tree problems to give similar approximation guarantees for the hitting-set versions of robust min-cut and shortest path problems respectively.