NDLI: Thresholded covering algorithms for robust and max

Content Provider	Springer Nature Link
Author	Nagarajan, Viswanath Gupta, Anupam Ravi, R.
Copyright Year	2013
Abstract	In a two-stage robust covering problem, one of several possible scenarios will appear tomorrow and require to be covered, but costs are higher tomorrow than today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? We consider the $$k$$ -robust model where the possible scenarios tomorrow are given by all demand-subsets of size $$k$$ . In this paper, we give the following simple and intuitive template for $$k$$ -robust covering problems: having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat. We show that this template gives good approximation algorithms for $$k$$ -robust versions of many standard covering problems: set cover, Steiner tree, Steiner forest, minimum-cut and multicut. Our $$k$$ -robust approximation ratios nearly match the best bounds known for their deterministic counterparts. The main technical contribution lies in proving certain net-type properties for these covering problems, which are based on dual-rounding and primal–dual ideas; these properties might be of some independent interest. As a by-product of our techniques, we also get algorithms for max–min problems of the form: “given a covering problem instance, which $$k$$ of the elements are costliest to cover?” For the problems mentioned above, we show that their $$k$$ -max–min versions have performance guarantees similar to those for the $$k$$ -robust problems.
Ending Page	615
Page Count	33
Starting Page	583
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	146
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-08-21
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Methods in Physics Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Theoretical, Mathematical and Computational Physics Approximation algorithms Graph algorithms Combinatorial optimization Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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