On Facility Location with General Lower Bounds

Shi, Li

doi:10.1137/1.9781611975482.138

Cited by 20 publications

(13 citation statements)

References 29 publications

(43 reference statements)

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“…The factor was improved to 82.6 by Ahmadian and Swamy [1]. Shi Li [11] gave the first constant factor approximation for general lower bounds, with the constant being large (4000). Han et al [7] studied the general lower bounded k-facility location (LBkFL) violating the lower bounds.…”

Section: Related Workmentioning

confidence: 99%

On Variants of Facility Location Problem with Outliers

Dabas,

Gupta

2021

Preprint

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In this work, we study the extension of two variants of the facility location problem (FL) to make them robust towards a few distantly located clients. First, k-facility location problem (kFL), a common generalization of FL and k median problems, is a well studied problem in literature. In the second variant, lower bounded facility location (LBFL), we are given a bound on the minimum number of clients that an opened facility must serve. Lower bounds are required in many applications like profitability in commerce and load balancing in transportation problem. In both the cases, the cost of the solution may be increased grossly by a few distantly located clients, called the outliers. Thus, in this work, we extend kFL and LBFL to make them robust towards the outliers. For kFL with outliers (kFLO) we present the first (constant) factor approximation violating the cardinality requirement by +1. As a by-product, we also obtain the first approximation for FLO based on LP-rounding. For LBFLO, we present a tri-criteria solution with a trade-off between the violations in lower bounds and the number of outliers. With a violation of 1/2 in lower bounds, we get a violation of 2 in outliers.

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Section: Related Workmentioning

confidence: 99%

On Variants of Facility Location Problem with Outliers

Dabas,

Gupta

2021

Preprint

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“…Ahmadian 和 Swamy [108] 通过归约到有更特殊结构的容量约束设施选址问题, 将上面的近似比改进到 82.6. 对于一般情形 (下界不要求一致), Li [109] 利用更复杂的归约, 给出了非一致下界约束的设施选址问题的第一个常数近似比为 4,000 的算法. [110] 给出, 算法得到的解不超过 O(1) • OPT + poly(log(n), k, d).…”

Section: 带下界约束的 K-均值问题尚没有近似算法我们简要介绍与之相关的带下界约束的设施选址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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“…Similarly, in experiment design [PAAS + 19] clustering is a fundamental tool used to design study cohorts to reduce the interference effects among subjects, and in such cases size constraints are natural requirements. Moreover, when clustering is seen through the lenses of optimization as in facility location [Li19,EHPR13] minimum size constraints are needed to ensure the viability of the facilities opened. Clustering with minimum-size constraints [AKCFB16, BKBL07, SSR19, APF + 10, Arm11, DHHL17, DHHL17] and the related lower-bounded facility location problem [Li19,Svi10,AS16] have received wide attention in the approximation algorithms literature.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, when clustering is seen through the lenses of optimization as in facility location [Li19,EHPR13] minimum size constraints are needed to ensure the viability of the facilities opened. Clustering with minimum-size constraints [AKCFB16, BKBL07, SSR19, APF + 10, Arm11, DHHL17, DHHL17] and the related lower-bounded facility location problem [Li19,Svi10,AS16] have received wide attention in the approximation algorithms literature.…”

Section: Introductionmentioning

confidence: 99%

Massively Parallel and Dynamic Algorithms for Minimum Size Clustering

Epasto¹,

Mahdian²,

Mirrokni³

et al. 2021

Preprint

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Clustering of data in metric spaces is a fundamental problem and has many applications in data mining and it is often used as an unsupervised learning tool inside other machine learning systems. In many scenarios where we are concerned with the privacy implications of clustering users, clusters are required to have minimum-size constraint. A canonical example of min-size clustering is in enforcing anonymization and the protection of the privacy of user data. Our work is motivated by real-world applications (such as the Federated Learning of Cohorts project -FLoC) where a min size clustering algorithm needs to handle very large amount of data and the data may also changes over time. Thus efficient parallel or dynamic algorithms are desired.In this paper, we study the r-gather problem, a natural formulation of minimum-size clustering in metric spaces. The goal of r-gather is to partition n points into clusters such that each cluster has size at least r, and the maximum radius of the clusters is minimized. This additional constraint completely changes the algorithmic nature of the problem, and many clustering techniques fail. Also previous dynamic and parallel algorithms do not achieve desirable complexity. We propose algorithms both in the Massively Parallel Computation (MPC) model and in the dynamic setting. Our MPC algorithm handles input points from the Euclidean space R d . It computes an O(1)-approximate solution of r-gather in O(log ǫ n) rounds using total space O(n 1+γ • d) for arbitrarily small constants ǫ, γ > 0. In addition our algorithm is fully scalable, i.e., there is no lower bound on the memory per machine. Our dynamic algorithm maintains an O(1)-approximate r-gather solution under insertions/deletions of points in a metric space with doubling dimension d. The update time is r∆, where ∆ is the ratio between the largest and the smallest distance.To obtain our results, we reveal connections between r-gather and r-nearest neighbors and provide several geometric and graph algorithmic tools including a near neighbor graph construction, and results on the maximal independent set / ruling set of the power graph in the MPC model, which might be both of independent interest. To show their generality, we extend our algorithm to solve several variants of r-gather in the MPC model, including r-gather with outliers and r-gather with total distance cost. Finally, we show effectiveness of these algorithmic techniques via a preliminary empirical study for FLoC application.

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On Facility Location with General Lower Bounds

Cited by 20 publications

References 29 publications

On Variants of Facility Location Problem with Outliers

On Variants of Facility Location Problem with Outliers

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

Massively Parallel and Dynamic Algorithms for Minimum Size Clustering

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