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The Non-Uniform k-Center Problem [article]

Deeparnab Chakrabarty, Prachi Goyal, Ravishankar Krishnaswamy
2016 arXiv   pre-print
In this paper, we introduce and study the Non-Uniform k-Center problem (NUkC).  ...  The NUkC problem generalizes the classic k-center problem when all the k radii are the same (which can be assumed to be 1 after scaling).  ...  Differing speeds, however, leads to non-uniformity, thus motivating the titular problem we consider. Definition 1.1 (The Non-Uniform k-Center Problem (NUkC)).  ... 
arXiv:1605.03692v2 fatcat:szq2pqgmzrgpbpxwdn7t7mx2mu

The Non-Uniform k-Center Problem

Deeparnab Chakrabarty, Prachi Goyal, Ravishankar Krishnaswamy
unpublished
In this paper, we introduce and study the Non-Uniform k-Center (NUkC) problem.  ...  The NUkC problem generalizes the classic k-center problem when all the k radii are the same (which can be assumed to be 1 after scaling).  ...  For a leaf 67:6 The Non-Uniform k-Center Problem node v, we let P v denote the vertex set of the unique leaf-root path excluding the root. min α ∀v ∈ L, u∈Pv y u ≥ 1 (RMFC-T LP) ∀t ∈ 1, · · · , h u∈Lt  ... 
fatcat:rcbjio2x2zbwpgahanaa7yevnu

Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem

José Alejandro Cornejo Acosta, Jesús García Díaz, Ricardo Menchaca-Méndez, Rolando Menchaca-Méndez
2020 Mathematics  
The goal of this paper is to explicitly state how the capacitated vertex k-center problem and the minimum capacitated dominating set problem are related.  ...  The capacitated vertex k-center problem receives as input a complete weighted graph and a set of capacity constraints.  ...  The authors also acknowledge Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE) and Consejo Nacional de Ciencia y Tecnología (CONACYT) for providing the necessary resources for the development  ... 
doi:10.3390/math8091551 fatcat:dncgwqff3nhp7jbuptpplpuz3y

LP Rounding for k-Centers with Non-uniform Hard Capacities

Marek Cygan, MohammadTaghi Hajiaghayi, Samir Khuller
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science  
In this paper we consider a generalization of the classical k-center problem with capacities.  ...  Our algorithm uses an LP rounding approach to solve this problem, and works for the case of non-uniform hard capacities, when multiple copies of a node may not be chosen and can be extended to the case  ...  By a reduction from the cost k-center problem [9] one can show that there is no (3 − )-approximation for the capacitated k-center problem with non-uniform capacities.  ... 
doi:10.1109/focs.2012.63 dblp:conf/focs/CyganHK12 fatcat:mvs4xcfnrzezblipniijfsosxm

Privacy Preserving Clustering with Constraints

Clemens Rösner, Melanie Schmidt, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
The k-center problem is a classical combinatorial optimization problem which asks to find k centers such that the maximum distance of any input point in a set P to its assigned center is minimized.  ...  The problem allows for elegant 2-approximations. However, the situation becomes significantly more difficult when constraints are added to the problem.  ...  The private k-center problem is introduced and 2-approximated in [3], and non-uniform lower bounds are studied in [4] .  ... 
doi:10.4230/lipics.icalp.2018.96 dblp:conf/icalp/Rosner018 fatcat:45ap4hrdefg33nrovc6mcemnzi

Comparing synopsis techniques for approximate spatial data analysis

A. B. Siddique, Ahmed Eldawy, Vagelis Hristidis
2019 Proceedings of the VLDB Endowment  
This paper experimentally studies four spatial data synopsis techniques for three common data analysis problems, namely, selectivity estimation, k-means clustering, and spatial partitioning.  ...  For each of the three problems, we compare with baseline techniques that operate on the whole dataset and evaluate the synopsis generation time, the time for computing an approximate answer on the synopsis  ...  KC-UH, KC-NH: Clustering on Uniform/ Non-uniform Histograms The input to this variant of K-Means++ is a 2d array of size r × c, and the number of clusters K.  ... 
doi:10.14778/3342263.3342635 fatcat:pnck7eixezg6lmovat3oy4ushe

Modeling and Practical Evaluation of a Service Location Problem in Large Scale Networks

Olivier Beaumont, Nicolas Bonichon, Hubert Larchevêque
2011 2011 International Conference on Parallel Processing  
We show how to turn an approximation algorithm for BPDC into an approximation algorithm for the non-uniform capacitated K-center problem and vice-versa.  ...  We consider a generalization of a classical optimization problem related to server and replica location problems in networks.  ...  Let K = (S, d, w, K) be an instance of the non-uniform capacitated K-center problem.  ... 
doi:10.1109/icpp.2011.36 dblp:conf/icpp/BeaumontBL11 fatcat:5nytw3vbj5fb3epzjuysjulwqu

A Non-Uniform-Angular-Rate Beam-Scan Method for Airborne TOPS Mode

Y. F. Guan, W. G. Chang
2018 Radioengineering  
Aiming at airborne SAR (Synthetic Aperture Radar) system, the Doppler characteristic of azimuthal echo of the TOPS mode with large scanning angle is analyzed, and a non-uniform-angular-rate beam-scan method  ...  TOPS (Terrain Observation by Progressive Scans) mode can achieve large scene coverage through the beam-scan in a uniform-angular-rate form; when the scanning angle is large, the variation of azimuth theoretical  ...  The Problem of Uniform Beam-scan TOPS mode can be assumed to be a constant rotation of the beam centered on a virtual rotation center, as shown in Fig. 1 .  ... 
doi:10.13164/re.2018.0876 fatcat:tf4inncp3feklcxrjubmgcisly

Constant factor approximations for Lower and Upper bounded Clusterings [article]

Neelima Gupta, Sapna Grover, Rajni Dabas
2022 arXiv   pre-print
We also present a result on LUkC with uniform upper bounds and, its generalization, lower and (uniform) upper bounded k supplier problem (LUkS).  ...  of upper bounds in solutions of upper bounded k-median and k-facility location problems respectively.  ...  In the k-center problem, the set of data points is same as the set of centers i.e., the centers can be opened at the data points. k-supplier (kS) is a generalization of the k-center problem in which the  ... 
arXiv:2203.14058v1 fatcat:7kilgacltbh4ldiywf2brgbtvi

Direct 3-D Sparse Imaging Using Non-Uniform Samples Without Data Interpolation

Sun, Pang, Xing, Li, Wang
2020 Electronics  
In this paper, we directly regard the imaging problem as a joint sparse reconstruction problem from non-uniform data without interpolation in 3-D space.  ...  Although data interpolation in k-space and fast Fourier transform have been employed in the existing 3-D sparse imaging methods to reduce the computational complexity, the data-gridding errors induced  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/electronics9020321 fatcat:72clupva5jefze2xif4lrkrmsa

Privacy preserving clustering with constraints [article]

Clemens Rösner, Melanie Schmidt
2018 arXiv   pre-print
The k-center problem is a classical combinatorial optimization problem which asks to find k centers such that the maximum distance of any input point in a set P to its assigned center is minimized.  ...  The problem allows for elegant 2-approximations. However, the situation becomes significantly more difficult when constraints are added to the problem.  ...  For the k-center problem we use the 9-approximation by [16] for the problem with uniform lower bound and non uniform upper bounds and the 6-approximation by [16] for the problem with uniform lower  ... 
arXiv:1802.02497v2 fatcat:cwgzfqq5ozbkbdiaooob5deplq

A Unified Framework for Clustering Constrained Data without Locality Property [chapter]

Hu Ding, Jinhui Xu
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
k-centers and 4-approx. for metric k-cellulars; (4 + ✏)-approx. for k-centers in constant dimensional space capacitated clustering 6 and 7-approx. for metric k-centers with uniform and non-uniform capacities  ...  in R d ; (1 + ✏)-approx. for 2-center in R 2 fault tolerant clustering 4 and 93-approx. for uniform and non-uniform metric k-median; 2-approx. for metric k-centers; r-gather clustering 2-approx. for metric  ...  Can the unified framework be applied to other types of k-CMeans/CMedian? Can it be extended to some non-Euclidean space? How to improve the selection algorithms? Thank You! Any Question?  ... 
doi:10.1137/1.9781611973730.97 dblp:conf/soda/DingX15 fatcat:h5odt42wwrbwxegrg4sjneklgi

Achieving anonymity via weak lower bound constraints for k-median and k-means [article]

Anna Arutyunova, Melanie Schmidt
2020 arXiv   pre-print
In addition to the point set P and the number of centers k, a k-clustering problem with (uniform) lower bounds gets a number B.  ...  We study k-clustering problems with lower bounds, including k-median and k-means clustering with lower bounds.  ...  There exist polynomial-time O(1)-approximation algorithms for the k-median problem with uniform and non-uniform lower bounds.  ... 
arXiv:2009.03078v2 fatcat:7xd7252l5zbkplje6g4npp7eha

LP Rounding for k-Centers with Non-uniform Hard Capacities [article]

Marek Cygan, MohammadTaghi Hajiaghayi, Samir Khuller
2012 arXiv   pre-print
In this paper we consider a generalization of the classical k-center problem with capacities.  ...  In addition we establish a lower bound on the integrality gap of 7(5) for non-uniform (uniform) hard capacities.  ...  By a reduction from the cost k-center problem [8] one can show that there is no (3 − )-approximation for the capacitated k-center problem with non-uniform capacities.  ... 
arXiv:1208.3054v1 fatcat:5esduijwuzc4bfdsjzwg4cicpa

Application of inverse problem algorithm for temperature uniformity in rapid thermal processing

Senpuu Lin, Hsin-Sen Chu
2002 Thin Solid Films  
Our numerical results indicate that temperature non-uniformity occurring during the ramp increase with the ramp-up rate.  ...  This article presents a finite-difference-method formulation to the application of inverse problem algorithms for uniform temperature tracking of several different linear ramp-up rates in rapid thermal  ...  Flow chart to the application of inverse problem algorithm. K) were performed to examine the wafer temperature non-uniformity during RTP as a function of the rampup rate.  ... 
doi:10.1016/s0040-6090(01)01630-3 fatcat:dtphklczqncw3dai27bvfilaqa
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