A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The Non-Uniform k-Center Problem
[article]

2016
*
arXiv
*
pre-print

In this paper, we introduce and study

arXiv:1605.03692v2
fatcat:szq2pqgmzrgpbpxwdn7t7mx2mu
*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)). ...##
###
The Non-Uniform k-Center Problem

unpublished

In this paper, we introduce and study

fatcat:rcbjio2x2zbwpgahanaa7yevnu
*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 ...##
###
Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem

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 ...

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

2012
*
2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
*

In this paper we consider a generalization of

doi:10.1109/focs.2012.63
dblp:conf/focs/CyganHK12
fatcat:mvs4xcfnrzezblipniijfsosxm
*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. ...##
###
Privacy Preserving Clustering with Constraints

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] . ...

##
###
Comparing synopsis techniques for approximate spatial data analysis

2019
*
Proceedings of the VLDB Endowment
*

This paper experimentally studies four spatial data synopsis techniques for three common data analysis

doi:10.14778/3342263.3342635
fatcat:pnck7eixezg6lmovat3oy4ushe
*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*. ...##
###
Modeling and Practical Evaluation of a Service Location Problem in Large Scale Networks

2011
*
2011 International Conference on Parallel Processing
*

We show how to turn an approximation algorithm for BPDC into an approximation algorithm for

doi:10.1109/icpp.2011.36
dblp:conf/icpp/BeaumontBL11
fatcat:5nytw3vbj5fb3epzjuysjulwqu
*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*. ...##
###
A Non-Uniform-Angular-Rate Beam-Scan Method for Airborne TOPS Mode

2018
*
Radioengineering
*

Aiming at airborne SAR (Synthetic Aperture Radar) system,

doi:10.13164/re.2018.0876
fatcat:tf4inncp3feklcxrjubmgcisly
*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 . ...##
###
Constant factor approximations for Lower and Upper bounded Clusterings
[article]

2022
*
arXiv
*
pre-print

We also present a result on LUkC with

arXiv:2203.14058v1
fatcat:7kilgacltbh4ldiywf2brgbtvi
*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*...##
###
Direct 3-D Sparse Imaging Using Non-Uniform Samples Without Data Interpolation

2020
*
Electronics
*

In this paper, we directly regard

doi:10.3390/electronics9020321
fatcat:72clupva5jefze2xif4lrkrmsa
*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. ...##
###
Privacy preserving clustering with constraints
[article]

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 ...

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

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? ...

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

2020
*
arXiv
*
pre-print

In addition to

arXiv:2009.03078v2
fatcat:7xd7252l5zbkplje6g4npp7eha
*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. ...##
###
LP Rounding for k-Centers with Non-uniform Hard Capacities
[article]

2012
*
arXiv
*
pre-print

In this paper we consider a generalization of

arXiv:1208.3054v1
fatcat:5esduijwuzc4bfdsjzwg4cicpa
*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. ...##
###
Application of inverse problem algorithm for temperature uniformity in rapid thermal processing

2002
*
Thin Solid Films
*

Our numerical results indicate that temperature

doi:10.1016/s0040-6090(01)01630-3
fatcat:dtphklczqncw3dai27bvfilaqa
*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. ...
« Previous

*Showing results 1 — 15 out of 508,938 results*