research-article

Robust and MaxMin Optimization under Matroid and Knapsack Uncertainty Sets

Authors:

Viswanath Nagarajan,

R. RaviAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 12, Issue 1

Article No.: 10, Pages 1 - 21

https://doi.org/10.1145/2746226

Published: 16 November 2015 Publication History

Abstract

Consider the following problem: given a set system (U, Ω) and an edge-weighted graph G = (U, E) on the same universe U, find the set A ∈ Ω such that the Steiner tree cost with terminals A is as large as possible—“which set in Ω is the most difficult to connect up?” This is an example of a max-min problem: find the set A ∈ Ω such that the value of some minimization (covering) problem is as large as possible.

In this article, we show that for certain covering problems that admit good deterministic online algorithms, we can give good algorithms for max-min optimization when the set system Ω is given by a p-system or knapsack constraints or both. This result is similar to results for constrained maximization of submodular functions. Although many natural covering problems are not even approximately submodular, we show that one can use properties of the online algorithm as a surrogate for submodularity.

Moreover, we give stronger connections between max-min optimization and two-stage robust optimization, and hence give improved algorithms for robust versions of various covering problems, for cases where the uncertainty sets are given by p-systems and knapsack constraints.

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Cited By

El Housni OFoussoul AGoyal V(2024)LP-based approximations for disjoint bilinear and two-stage adjustable robust optimizationMathematical Programming: Series A and B10.1007/s10107-023-02004-9206:1-2(239-281)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s10107-023-02004-9
Luo QNagarajan VSundt AYin YVincent JShahabi M(2023)Efficient Algorithms for Stochastic Ride-Pooling Assignment with Mixed FleetsTransportation Science10.1287/trsc.2021.034957:4(908-936)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1287/trsc.2021.0349
Wu BHan K(2022)Fast Algorithm for Big Data Summarization with Knapsack and Partition Matroid Constraints2022 International Conference on INnovations in Intelligent SysTems and Applications (INISTA)10.1109/INISTA55318.2022.9894252(1-6)Online publication date: 8-Aug-2022
https://doi.org/10.1109/INISTA55318.2022.9894252
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Index Terms

Robust and MaxMin Optimization under Matroid and Knapsack Uncertainty Sets
1. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 12, Issue 1

Special Issue on SODA'12 and Regular Papers

February 2016

243 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2846103

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2015 ACM.

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Association for Computing Machinery

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Publication History

Published: 16 November 2015

Accepted: 01 March 2015

Revised: 01 April 2012

Received: 01 February 2011

Published in TALG Volume 12, Issue 1

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Cited By

El Housni OFoussoul AGoyal V(2024)LP-based approximations for disjoint bilinear and two-stage adjustable robust optimizationMathematical Programming: Series A and B10.1007/s10107-023-02004-9206:1-2(239-281)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s10107-023-02004-9
Luo QNagarajan VSundt AYin YVincent JShahabi M(2023)Efficient Algorithms for Stochastic Ride-Pooling Assignment with Mixed FleetsTransportation Science10.1287/trsc.2021.034957:4(908-936)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1287/trsc.2021.0349
Wu BHan K(2022)Fast Algorithm for Big Data Summarization with Knapsack and Partition Matroid Constraints2022 International Conference on INnovations in Intelligent SysTems and Applications (INISTA)10.1109/INISTA55318.2022.9894252(1-6)Online publication date: 8-Aug-2022
https://doi.org/10.1109/INISTA55318.2022.9894252
Ito TKakimura NKamiyama NKobayashi YOkamoto Y(2022)A Parameterized View to the Robust Recoverable Base Problem of Matroids Under Structural UncertaintyOperations Research Letters10.1016/j.orl.2022.05.001Online publication date: May-2022
https://doi.org/10.1016/j.orl.2022.05.001
Housni OFoussoul AGoyal V(2022)LP-Based Approximations for Disjoint Bilinear and Two-Stage Adjustable Robust OptimizationInteger Programming and Combinatorial Optimization10.1007/978-3-031-06901-7_17(223-236)Online publication date: 27-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-06901-7_17
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https://doi.org/10.1287/moor.2020.1082
Linhares ASwamy CCharikar MCohen E(2019)Approximation algorithms for distributionally-robust stochastic optimization with black-box distributionsProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316391(768-779)Online publication date: 23-Jun-2019
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Poularakis KIosifidis GSmaragdakis GTassiulas L(2019)Optimizing Gradual SDN Upgrades in ISP NetworksIEEE/ACM Transactions on Networking10.1109/TNET.2018.289024827:1(288-301)Online publication date: 1-Feb-2019
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Linhares AOlver NSwamy CZenklusen R(2019)Approximate Multi-matroid Intersection via Iterative RefinementInteger Programming and Combinatorial Optimization10.1007/978-3-030-17953-3_23(299-312)Online publication date: 22-May-2019
https://dl.acm.org/doi/10.1007/978-3-030-17953-3_23
Sarpatwar KSchieber BShachnai H(2018)Constrained submodular maximization via greedy local searchOperations Research Letters10.1016/j.orl.2018.11.002Online publication date: Nov-2018
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