Improved Approximation Algorithms for Capacitated Fault-Tolerant k-Center

Fernandes, Cristina G.; Paula, Samuel P. de; Pedrosa, Lehilton L. C.

doi:10.1007/978-3-662-49529-2_33

Cited by 4 publications

(2 citation statements)

References 17 publications

(19 reference statements)

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“…For the conservative capacitated fault-tolerant model, only those points that had been assigned to faulty centers may be reassigned. Under uniform version, Fernandes et al [9] improved these results to 6-approximation and 7-approximation respectively. They also gave the first constant approximations for the non-uniform capacitated and conservative fault-tolerant k-center clustering.…”

Section: Ruiqi Yang Dachuan Xu Yicheng Xu and Dongmei Zhangmentioning

confidence: 99%

An adaptive probabilistic algorithm for online <i>k</i>-center clustering

Yang¹,

Xu²,

Xu³

et al. 2019

Journal of Industrial &Amp; Management Optimization

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The k-center clustering is one of the well-studied clustering problems in computer science. We are given a set of data points P ⊆ R d , where R d is d dimensional Euclidean space. We need to select k ≤ |P | points as centers and partition the set P into k clusters with each point connecting to its nearest center. The goal is to minimize the maximum radius. We consider the so-called online k-center clustering model where the data points in R d arrive over time. We present the bi-criteria (n k , (log U * L *) 2)-competitive algorithm and (n k , log γ log nγ k)-competitive algorithm for semi-online and fully-online kcenter clustering respectively, where U * is the maximum cluster radius of optimal solution, L * is the minimum distance of two distinct points of P , γ is the ratio of the maximum distance of two distinct points and the minimum distance of two distinct points of P and n is the number of points that will arrive in total.

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Section: Ruiqi Yang Dachuan Xu Yicheng Xu and Dongmei Zhangmentioning

confidence: 99%

An adaptive probabilistic algorithm for online <i>k</i>-center clustering

Yang¹,

Xu²,

Xu³

et al. 2019

Journal of Industrial &Amp; Management Optimization

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show abstract

“…The constant factor was later improved to 9 by An et al [2]. Other variants of the capacitated k-center problem have been also studied in the literature (see, e.g., [6,[9][10][11]13]).…”

Section: Introductionmentioning

confidence: 99%

Improved Algorithms for Distributed Balanced Clustering

Mirjalali

Zarrabi-Zadeh

2020

Lecture Notes in Computer Science

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We study a weighted balanced version of the k-center problem, where each center has a fixed capacity, and each element has an arbitrary demand. The objective is to assign demands of the elements to the centers, so as the total demand assigned to each center does not exceed its capacity, while the maximum distance between centers and their assigned elements is minimized. We present a deterministic O(1)-approximation algorithm for this generalized version of the k-center problem in the distributed setting, where data is partitioned among a number of machines. Our algorithm substantially improves the approximation factor of the current best randomized algorithm available for the problem. We also show that the approximation factor of our algorithm can be improved to 5 + ε, when the underlying metric space has a bounded doubling dimension.

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Capacitated Center Problems with Two-Sided Bounds and Outliers

Ding

Huang

et al. 2017

Lecture Notes in Computer Science

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In recent years, the capacitated center problems have attracted a lot of research interest. Given a set of vertices V , we want to find a subset of vertices S, called centers, such that the maximum cluster radius is minimized. Moreover, each center in S should satisfy some capacity constraint, which could be an upper or lower bound on the number of vertices it can serve. Capacitated k-center problems with one-sided bounds (upper or lower) have been well studied in previous work, and a constant factor approximation was obtained.We are the first to study the capacitated center problem with both capacity lower and upper bounds (with or without outliers). We assume each vertex has a uniform lower bound and a non-uniform upper bound. For the case of opening exactly k centers, we note that a generalization of a recent LP approach can achieve constant factor approximation algorithms for our problems. Our main contribution is a simple combinatorial algorithm for the case where there is no cardinality constraint on the number of open centers. Our combinatorial algorithm is simpler and achieves better constant approximation factor compared to the LP approach.

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Improved Approximation Algorithms for Capacitated Fault-Tolerant k-Center

Cited by 4 publications

References 17 publications

An adaptive probabilistic algorithm for online <i>k</i>-center clustering

An adaptive probabilistic algorithm for online <i>k</i>-center clustering

Improved Algorithms for Distributed Balanced Clustering

Capacitated Center Problems with Two-Sided Bounds and Outliers

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