Thrifty algorithms for multistage robust optimization

Anupam Gupta, Viswanath Nagarajan, Vijay V. Vazirani

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 k1 > k2 > ⋯ > 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 + log n)-approximation algorithm, nearly matching the Ω(log n + log m/log log m) 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, log n, log λmax}), where λmax is the maximum inflation over all the stages. We conjecture that these problems also admit O(1)-approximate thrifty algorithms.

Original languageEnglish (US)
Title of host publicationInteger Programming and Combinatorial Optimization - 16th International Conference, IPCO 2013, Proceedings
Number of pages12
StatePublished - 2013
Event16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013 - Valparaiso, Chile
Duration: Mar 18 2013Mar 20 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7801 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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