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Fault-tolerant facility location

Published: 22 August 2008 Publication History

Abstract

We consider a fault-tolerant generalization of the classical uncapacitated facility location problem, where each client j has a requirement that rj distinct facilities serve it, instead of just one. We give a 2.076-approximation algorithm for this problem using LP rounding, which is currently the best-known performance guarantee. Our algorithm exploits primal and dual complementary slackness conditions and is based on clustered randomized rounding. A technical difficulty that we overcome is the presence of terms with negative coefficients in the dual objective function, which makes it difficult to bound the cost in terms of dual variables. For the case where all requirements are the same, we give a primal-dual 1.52-approximation algorithm.
We also consider a fault-tolerant version of the k-median problem. In the metric k-median problem, we are given n points in a metric space. We must select k of these to be centers, and then assign each input point j to the selected center that is closest to it. In the fault-tolerant version we want j to be assigned to rj distinct centers. The goal is to select the k centers so as to minimize the sum of assignment costs. The primal-dual algorithm for fault-tolerant facility location with uniform requirements also yields a 4-approximation algorithm for the fault-tolerant k-median problem for this case. This the first constant-factor approximation algorithm for the uniform requirements case.

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    Published In

    cover image ACM Transactions on Algorithms
    ACM Transactions on Algorithms  Volume 4, Issue 4
    August 2008
    264 pages
    ISSN:1549-6325
    EISSN:1549-6333
    DOI:10.1145/1383369
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 22 August 2008
    Accepted: 01 October 2007
    Revised: 01 September 2007
    Received: 01 August 2005
    Published in TALG Volume 4, Issue 4

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    Author Tags

    1. k-median problem
    2. Approximation algorithms
    3. facility location

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    • (2024) How to locate services optimizing redundancy: A comparative analysis of -Covering Facility Location models Socio-Economic Planning Sciences10.1016/j.seps.2024.10193894(101938)Online publication date: Aug-2024
    • (2024)Multi-neighborhood simulated annealing for the capacitated facility location problem with customer incompatibilitiesComputers & Industrial Engineering10.1016/j.cie.2023.109858188(109858)Online publication date: Mar-2024
    • (2024)Approximation algorithms for the fault-tolerant facility location problem with submodular penaltiesJournal of Combinatorial Optimization10.1007/s10878-024-01106-047:2Online publication date: 26-Feb-2024
    • (2024)Speeding Up Constrained k-Means Through 2-MeansAlgorithmic Aspects in Information and Management10.1007/978-981-97-7801-0_5(52-63)Online publication date: 21-Sep-2024
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    • (2022)FT-KMEANS: A Fast Algorithm For Fault-Tolerant Facility Location2022 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)10.1109/IEEM55944.2022.9989850(0502-0506)Online publication date: 7-Dec-2022
    • (2022)Hotelling games in fault-prone settingsTheoretical Computer Science10.1016/j.tcs.2022.04.013Online publication date: Apr-2022
    • (2022)Constant approximation for fault-tolerant median problems via iterative roundingOperations Research Letters10.1016/j.orl.2022.05.00250:4(384-390)Online publication date: 1-Jul-2022
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