Approximation Schemes for Capacitated Clustering in Doubling Metrics

Cohen-Addad, Vincent

doi:10.1137/1.9781611975994.138

Cited by 23 publications

(14 citation statements)

References 30 publications

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“…Furthermore, the running time has a near-linear dependency on n and does not depend exponentially on d. A comparison with the running time of the previous (1 + )-approximation algorithms can be found in Table 3. We also obtain FPT (1 + )-approximation algorithms with parameter k for the Euclidean version of several other problems including capacitated clustering [35,33] and lower-bounded clustering. We note that these are the first (1+ )-approximations for these problems with near-linear dependency on n. For Euclidean capacitated clustering, quadratic time FPT algorithms follow due to [40,16] (see Table 4).…”

Section: Theorem 11 (Informal)mentioning

confidence: 99%

“…We note that these are the first (1+ )-approximations for these problems with near-linear dependency on n. For Euclidean capacitated clustering, quadratic time FPT algorithms follow due to [40,16] (see Table 4). Also, the (1+ )-approximation for Euclidean capacitated clustering in [35] and [33] have running time (k −1 ) k −O (1) n O (1) and at least n −O (1) (see Table 4).…”

Section: Theorem 11 (Informal)mentioning

confidence: 99%

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On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications

Bandyapadhyay,

Fomin,

Simonov

2020

Preprint

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Fair clustering is a constrained variant of clustering where the goal is to partition a set of colored points, such that the fraction of points of any color in every cluster is more or less equal to the fraction of points of this color in the dataset. This variant was recently introduced by Chierichetti et al. [NeurIPS, 2017] in a seminal work and became widely popular in the clustering literature. In this paper, we propose a new construction of coresets for fair clustering based on random sampling. The new construction allows us to obtain the first coreset for fair clustering in general metric spaces. For Euclidean spaces, we obtain the first coreset whose size does not depend exponentially on the dimension. Our coreset results solve open questions proposed by Schmidt et al. [WAOA, 2019] and Huang et al. [NeurIPS, 2019].The new coreset construction helps to design several new approximation and streaming algorithms. In particular, we obtain the first true constant-approximation algorithm for metric fair clustering, whose running time is fixed-parameter tractable (FPT). In the Euclidean case, we derive the first (1+ )-approximation algorithm for fair clustering whose time complexity is near-linear and does not depend exponentially on the dimension of the space. Besides, our coreset construction scheme is fairly general and gives rise to coresets for a wide range of constrained clustering problems. This leads to improved constant-approximations for these problems in general metrics and near-linear time (1 + )-approximations in the Euclidean metric.

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Section: Theorem 11 (Informal)mentioning

confidence: 99%

Section: Theorem 11 (Informal)mentioning

confidence: 99%

On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications

Bandyapadhyay,

Fomin,

Simonov

2020

Preprint

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“…结合 Kumar 等 [51] 的技巧, Cohen-Addad 和 Li [106] 给出了运行时间为 (k/ϵ) k(1/ϵ) O (1) n O(1) (与 d 无关) 的 PTAS. Cohen-Addad [8] 给出了运行时间为 n ((2/ϵ) 2 log n) O (d) (与 k 无关) 的 PTAS.…”

Section: 带约束的 K K K-均值问题unclassified

A survey on theory and algorithms for bm$k$-means problems

Zhang¹,

Li²,

Dachuan³

et al. 2020

Sci. Sin.-Math.

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“…Clustering problems are studied due to their widespread applications in operations research and machine learning areas [7,8,12,13,14,22,26]. As a consequence, some natural and significant variants also attract lots of research interests [10,18,19,21,28,29].…”

Section: Introductionmentioning

confidence: 99%

Approximate the individually fair k-center with outliers

Han¹,

Xu²,

Xu³

et al. 2022

Preprint

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In this paper, we propose and investigate the individually fair kcenter with outliers (IFkCO). In the IFkCO, we are given an n-sized vertex set in a metric space, as well as integers k and q. At most k vertices can be selected as the centers and at most q vertices can be selected as the outliers. The centers are selected to serve all the not-an-outlier (i.e., served) vertices. The so-called individual fairness constraint restricts that every served vertex must have a selected center not too far way. More precisely, it is supposed that there exists at least one center among its (n−q)/k closest neighbors for every served vertex. Because every center serves (n − q)/k vertices on the average. The objective is to select centers and outliers, assign every served vertex to some center, so as to minimize the maximum fairness ratio over all served vertices, where the fairness ratio of a vertex is defined as the ratio between its distance with the assigned center and its distance with a (n − q)/k th closest neighbor. As our main contribution, a 4-approximation algorithm is presented, based on which we develop an improved algorithm from a practical perspective. Extensive experiment results on both synthetic datasets and real-

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Approximation Schemes for Capacitated Clustering in Doubling Metrics

Cited by 23 publications

References 30 publications

On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications

On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications

A survey on theory and algorithms for bm$k$-means problems

Approximate the individually fair k-center with outliers

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