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Exact and Approximation Algorithms for Clustering
, 1997
"... In this paper we present a n O(k1�1=d) time algorithm for solving the kcenter problem in R d, under L1 and L2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete kcenter problem, as well. We also describe a simple (1 +)approximation algorithm for the kcenter pr ..."
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Cited by 79 (6 self)
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problem, with running time O(n log k) + (k = ) O(k1�1=d). Finally, we present a n O(k1�1=d) time algorithm for solving the Lcapacitated kcenter problem, provided that L = (n=k 1�1=d) or L = O(1). We conclude with a simple approximation algorithm for the Lcapacitated kcenter problem.
Exact and Approximation Algorithms for Clustering (Extended Abstract)
, 1998
"... In this paper we present an n O(k 1\Gamma1=d ) time algorithm for solving the kcenter problem in R d , under L1 and L2 metrics. The algorithm extends to other metrics, and to the discrete kcenter problem. We also describe a simple (1+ ffl) approximation algorithm for the kcenter problem, ..."
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, with running time O(n log k) + (k=ffl) O(k 1\Gamma1=d ) . Finally, we present a n O(k 1\Gamma1=d ) time algorithm for solving the Lcapacitated k center problem, provided that L = \Omega\Gamma n=k 1\Gamma1=d ) or L = O(1). We conclude with a simple approximation algorithm for the Lcapacitated kcenter
The Capacitated KCenter Problem
 In Proceedings of the 4th Annual European Symposium on Algorithms, Lecture Notes in Computer Science 1136
, 1996
"... The capacitated Kcenter problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assign ..."
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Cited by 40 (6 self)
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The capacitated Kcenter problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may
An Efficient kMeans Clustering Algorithm: Analysis and Implementation
, 2000
"... Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its ..."
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Cited by 417 (4 self)
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Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its
Generalized kCenter Problems
"... The kcenter problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality, so that the maximum distance of any node to its nearest center is minimized. In this paper, we consider a generalization of this p ..."
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The kcenter problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality, so that the maximum distance of any node to its nearest center is minimized. In this paper, we consider a generalization
Asymmetry in kCenter Variants
, 2003
"... This paper explores three concepts: the kcenter problem, some of its variants, and asymmetry. The kcenter problem is a fundamental clustering problem, similar to the kmedian problem. Variants of kcenter may more accurately model reallife problems than the original formulation. Asymmetry is a ..."
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Cited by 3 (2 self)
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This paper explores three concepts: the kcenter problem, some of its variants, and asymmetry. The kcenter problem is a fundamental clustering problem, similar to the kmedian problem. Variants of kcenter may more accurately model reallife problems than the original formulation. Asymmetry is a
Fault Tolerant KCenter Problems
, 1997
"... The basic Kcenter problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. This problem is known to be NPhard, and se ..."
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Cited by 20 (1 self)
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The basic Kcenter problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. This problem is known to be NP
Approximation Algorithms for the KCenter
 Proc. OR 2002
, 2002
"... In this paper we deal with the vertex kcenter problem, a problem which is a part of the discrete location theory. Informally, given a set of cities, with intercity distances specified, one has to pick k cities and build warehouses in them so as to minimize the maximum distance of any city from its ..."
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In this paper we deal with the vertex kcenter problem, a problem which is a part of the discrete location theory. Informally, given a set of cities, with intercity distances specified, one has to pick k cities and build warehouses in them so as to minimize the maximum distance of any city from its
The pNeighbor kCenter Problem
, 1998
"... The kcenter problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality, so that the maximum distance of any node to its nearest center is minimized. In this paper, we consider a generalization of this p ..."
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Cited by 11 (0 self)
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The kcenter problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality, so that the maximum distance of any node to its nearest center is minimized. In this paper, we consider a generalization
kCenter problems with minimum coverage
, 2005
"... In this work, we study an extension of the kcenter facility location problem, where centers are required to service a minimum of clients. This problem is motivated by requirements to balance the workload of centers while allowing each center to cater to a spread of clients. We study three variants ..."
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Cited by 4 (1 self)
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In this work, we study an extension of the kcenter facility location problem, where centers are required to service a minimum of clients. This problem is motivated by requirements to balance the workload of centers while allowing each center to cater to a spread of clients. We study three variants
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