Approximation algorithms for the priority facility location problem with penalties

Wang, Fengmin; Xu, Dianguo; Wu, Chenchen

doi:10.1007/s11424-014-2157-2

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…For uncapacitated FLPP , a 3-factor approximation using primal dual techniques was given by Charikar et al [20] which was subsequently improved to 2 by Jain et al [16] using dual-fitting and greedy approach. Wang et al [23] also gave a 2-factor approximation using a combination of primal-dual and greedy technique. Later Xu and Xu [26] gave a 2 + 2/e using LP rounding.…”

Section: Related Workmentioning

confidence: 99%

“…A PTAS for FLPO was given by Friggstad et al [9] using multiswap local search for a restricted variant of the problem with uniform facility opening costs and doubling metrics. Recently, Wang et al [23] gave a 2 factor approximation using a combination of primal dual and greedy schema for the general setting. To the best of our knowledge, capacitated FLPO has not been studied earlier.…”

Section: Introductionmentioning

confidence: 99%

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Uniform Capacitated Facility Location Problems with Penalties/Outliers

Dabas,

Gupta

2020

Preprint

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In this paper, we present a framework to design approximation algorithms for capacitated facility location problems with penalties/outliers using LP-rounding. Primal-dual technique, which has been particularly successful in dealing with outliers and penalties, has not been very successful in dealing with capacities. For example, despite unbounded integrality gap for facility location problem with outliers(FLPO), Charikar et al. [20] were able to get around the hardness by guessing the maximum facility opening cost in the optimal and provide a primal-dual solution for the problem. On the other hand, no primal-dual solution has been able to break the hardness of capacitated facility location problem(CFLP). LP-rounding techniques had also not been very successful in dealing with capacities until a recent work by Grover et al. [10,11]. Their constant factor approximation violating the capacities by a small factor (1 + ) is promising while dealing with capacities. Though LP-rounding has not been very promising while dealing with penalties and outliers, we successfully apply it to deal with them along with capacities. That is, our results are obtained by rounding the solution to the natural LP once again exhibiting the power of LP-rounding technique. Solutions obtained by LP-rounding are easy to integrate with other LP-based algorithms.In this paper, we apply our framework to obtain first constant factor approximations for capacitated facility location problem with outlier (CFLPO) and capacitated k-facility location problem with penalty(CkFLPP) for hard uniform capacities using LP-rounding. Our solutions incur slight violations in capacities, (1 + ) for the problems without cardinality(k) constraint and (2 + ) for the problems with the cardinality constraint. For the outlier variant, we also incur a small loss (1 + ) in outliers. Due to the hardness of the underlying problems, the violations are inevitable. Thus we achieve the best possible by rounding the solution of natural LP for these problems. To the best of our knowledge, no results are known for CFLPO and CkFLPP. The only result known for CFLPP uses local search.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uniform Capacitated Facility Location Problems with Penalties/Outliers

Dabas,

Gupta

2020

Preprint

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“…Designing approximation algorithms for clustering with priorities remains an active area of research. For example, several constant factor approximation algorithms are known for the facility location objective [1][2][3]. Unfortunately, clustering with priorities remains elusive under the extensively studied k-median objective.…”

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confidence: 99%

An approximation algorithm for k-median with priorities

Zhang

et al. 2021

Sci. China Inf. Sci.

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Clustering is a fundamental problem in computer science. This problem is to partition a given set of clients into several clusters such that clients in the same cluster are more similar to each other. In many clustering applications, the clients are different in the levels of services they require. Motivated by such applications, Ravi and Sinha [1] introduced the problem of clustering with priorities, wherein each client is associated with a priority and can only be assigned to a facility opened at the same or higher priorities.

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