Approximation Algorithms for Cost-robust Discrete Minimization Problems Based on their LP-Relaxations

Khaled Elbassioni

doi:10.1007/s00453-022-00987-z

Approximation Algorithms for Cost-robust Discrete Minimization Problems Based on their LP-Relaxations

Khaled Elbassioni

Electrical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. Assuming the existence of an integrality gap verifier with a bounded approximation guarantee for the LP relaxation of the non-robust version of the problem, we derive approximation algorithms for the robust version under different types of uncertainty, including polyhedral and ellipsoidal uncertainty.

Original language	British English
Pages (from-to)	3622-3654
Number of pages	33
Journal	Algorithmica (New York)
Volume	84
Issue number	12
DOIs	https://doi.org/10.1007/s00453-022-00987-z
State	Published - Dec 2022

Keywords

Approximation algorithms
Discrete optimization
Linear programming
Randomized rounding
Robust optimization

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10.1007/s00453-022-00987-z

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title = "Approximation Algorithms for Cost-robust Discrete Minimization Problems Based on their LP-Relaxations",

abstract = "We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. Assuming the existence of an integrality gap verifier with a bounded approximation guarantee for the LP relaxation of the non-robust version of the problem, we derive approximation algorithms for the robust version under different types of uncertainty, including polyhedral and ellipsoidal uncertainty.",

keywords = "Approximation algorithms, Discrete optimization, Linear programming, Randomized rounding, Robust optimization",

author = "Khaled Elbassioni",

note = "Funding Information: K. Elbassioni: Partially supported by Abu Dhabi Education \& Knowledge-Abu Dhabi Award for Research Excellence (AARE18-152) Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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N2 - We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. Assuming the existence of an integrality gap verifier with a bounded approximation guarantee for the LP relaxation of the non-robust version of the problem, we derive approximation algorithms for the robust version under different types of uncertainty, including polyhedral and ellipsoidal uncertainty.

AB - We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. Assuming the existence of an integrality gap verifier with a bounded approximation guarantee for the LP relaxation of the non-robust version of the problem, we derive approximation algorithms for the robust version under different types of uncertainty, including polyhedral and ellipsoidal uncertainty.

KW - Approximation algorithms

KW - Discrete optimization

KW - Linear programming

KW - Randomized rounding

KW - Robust optimization

UR - https://www.scopus.com/pages/publications/85131529829

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JO - Algorithmica (New York)

JF - Algorithmica (New York)

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ER -

Approximation Algorithms for Cost-robust Discrete Minimization Problems Based on their LP-Relaxations

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Keywords

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