Thresholded Covering Algorithms for Robust and Max-min Optimization

13 years 9 months ago

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The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? For example, in a set cover instance, if any one of the n k subsets of the universe that have size k may appear tomorrow, what is a good course of action? Feige et al. [FJMM07], and later, Khandekar et al. [KKMS08], considered this k-robust model where the possible outcomes tomorrow are given by all demand-subsets of size k, and gave algorithms for the set cover problem, and the Steiner tree and facility location problems in this model, respectively. In this paper, we give the following simple and intuitive template for k-robust problems: having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold (which is ≈ Opt/k), augment the anticipatory solu...

Anupam Gupta, Viswanath Nagarajan, R. Ravi

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