Two-stage robust network design with exponential scenarios

Rohit Khandekar, Guy Kortsarz, Vahab Mirrokni, Mohammad R. Salavatipour

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

10 Scopus citations

Abstract

We study two-stage robust variants of combinatorial optimization problems like Steiner tree, Steiner forest, and uncapacitated facility location. The robust optimization problems, previously studied by Dhamdhere et al. [1], Golovin et al. [6], and Feige et al. [4], are two-stage planning problems in which the requirements are revealed after some decisions are taken in stage one. One has to then complete the solution, at a higher cost, to meet the given requirements. In the robust Steiner tree problem, for example, one buys some edges in stage one after which some terminals are revealed. In the second stage, one has to buy more edges, at a higher cost, to complete the stage one solution to build a Steiner tree on these terminals. The objective is to minimize the total cost under the worst-case scenario. In this paper, we focus on the case of exponentially many scenarios given implicitly. A scenario consists of any subset of k terminals (for Steiner tree), or any subset of k terminal-pairs (for Steiner forest), or any subset of k clients (for facility location). We present the first constant-factor approximation algorithms for the robust Steiner tree and robust uncapacitated facility location problems. For the robust Steiner forest problem with uniform inflation, we present an O(logn)-approximation and show that the problem with two inflation factors is impossible to approximate within O(log1/2 - ε n) factor, for any constant ε > 0, unless NP has randomized quasi-polynomial time algorithms. Finally, we show APX-hardness of the robust min-cut problem (even with singleton-set scenarios), resolving an open question by [1] and [6].

Original languageEnglish (US)
Title of host publicationAlgorithms - ESA 2008 - 16th Annual European Symposium, Proceedings
Pages589-600
Number of pages12
DOIs
StatePublished - Dec 24 2008
Event16th Annual European Symposium on Algorithms, ESA 2008 - Karlsruhe, Germany
Duration: Sep 15 2008Sep 17 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5193 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th Annual European Symposium on Algorithms, ESA 2008
CountryGermany
CityKarlsruhe
Period9/15/089/17/08

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Khandekar, R., Kortsarz, G., Mirrokni, V., & Salavatipour, M. R. (2008). Two-stage robust network design with exponential scenarios. In Algorithms - ESA 2008 - 16th Annual European Symposium, Proceedings (pp. 589-600). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5193 LNCS). https://doi.org/10.1007/978-3-540-87744-8-49