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Algorithms for Facility Location Problems with Outliers (Extended Abstract)
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms
, 2000
"... ) Moses Charikar Samir Khuller y David M. Mount z Giri Narasimhan x Abstract Facility location problems are traditionally investigated with the assumption that all the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called outlier ..."
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Cited by 68 (8 self)
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) Moses Charikar Samir Khuller y David M. Mount z Giri Narasimhan x Abstract Facility location problems are traditionally investigated with the assumption that all the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called outliers, can exert a disproportionately strong influence over the final solution. In this paper we explore a generalization of various facility location problems (Kcenter, Kmedian, uncapacitated facility location etc) to the case when only a specified fraction of the customers are to be served. What makes the problems harder is that we have to also select the subset that should get service. We provide generalizations of various approximation algorithms to deal with this added constraint. 1 Introduction The facility location problem and the related clustering problems, kmedian and kcenter, are widely studied in operations research and computer science [3, 7, 22, 24, 32]. Typically in...
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 34 (5 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 be assigned at most L vertices. This problem is known to be NPhard. We give polynomial time approximation algorithms for two different versions of this problem that achieve approximation factors of 5 and 6. We also study some generalizations of this problem. 1. Introduction The basic Kcenter problem is a fundamental facility location problem [17] and is defined as follows: given an edgeweighted graph G = (V; E) find a subset S ` V of size at most K such that each vertex in V is "close" to some vertex in S. More formally, the objective function is defined as follows: min S`V max u2V min v2S d(u; v) where d is the distance function. For example, one may wish to install K fire stations and mi...
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 15 (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 NPhard, and several optimal approximation algorithms that achieve a factor of 2 have been developed for it. We focus our attention on a generalization of this problem, where each vertex is required to have a set of ff (ff K) centers close to it. In particular, we study two different versions of this problem. In the first version, each vertex is required to have at least ff centers close to it. In the second version, each vertex that does not have a center placed on it is required to have at least ff centers close to it. For both these versions we are able to provide polynomial time approximation algorithms that achieve constant approximation factors for any ff. For the first version we give an algorithm ...
Solving the pCenter Problem with Tabu Search and Variable Neighborhood Search
, 2000
"... The pCenter problem consists in locating p facilities and assigning clients to them in order to minimize the maximum distance between a client and the facility to which he is allocated. In this paper we present a basic Variable Neighborhood Search and two Tabu Search heuristics for the pCenter ..."
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Cited by 11 (0 self)
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The pCenter problem consists in locating p facilities and assigning clients to them in order to minimize the maximum distance between a client and the facility to which he is allocated. In this paper we present a basic Variable Neighborhood Search and two Tabu Search heuristics for the pCenter problem without triangle inequality. Both proposed methods use the 1interchange (or vertex substitution) neighborhood structure.
Improved Algorithms for Fault Tolerant Facility Location
 In Symposium on Discrete Algorithms
, 2001
"... We consider a generalization of the classical facility location problem, where we require the solution to be faulttolerant. Every demand point j is served by r j facilities instead of just one. The facilities other than the closest one are "backup" facilities for that demand, and will be used only ..."
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Cited by 9 (2 self)
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We consider a generalization of the classical facility location problem, where we require the solution to be faulttolerant. Every demand point j is served by r j facilities instead of just one. The facilities other than the closest one are "backup" facilities for that demand, and will be used only if the closer facility (or the link to it) fails. Hence, for any demand, we assign nonincreasing weights to the routing costs to farther facilities. The cost of assignment for demand j is the weighted linear combination of the assignment costs to its r j closest open facilities. We wish to minimize the sum of the cost of opening the facilities and the assignment cost of each demand j. We obtain a factor 4 approximation to this problem through the application of various rounding techniques to the linear relaxation of an integer program formulation. We further improve this...
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 7 (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 of this problem where, given a number p, we wish to place k centers so as to minimize the maximum distance of any noncenter node to its p th closest center. We derive a best possible approximation algorithm for this problem. 1 Introduction The kcenter problem is a classical problem in facility location: given n cities and the distances between them, we wish to select k of these cities as centers so that the maximum distance of a city from its closest center is minimized. The problem is NPhard and Hochbaum and Shmoys present a 2approximation algorithm 1 for graphs with edge weights obeying triangle inequality [4]. Further they also show that no polynomial time algorithm for this problem ca...
Facility Location with Dynamic Distance Functions
"... Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating in ..."
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Cited by 5 (1 self)
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Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to traffic congestion the traversal time on links changes with time. Very often, we have some estimates as to how the edge lengths change over time, and our objective is to choose a set of locations (vertices) as centers, such that at every time instant each vertex has a center close to it (clearly, the center close to a vertex may change over time). We also provide approximation algorithms as well as hardness results for the Kcenter problem under this model. This is the first comprehensive study regarding approximation algorithms for facility location for good timeinvariant solutions. 1. Introduction Previous theoretical work on fac...
Approximation Algorithm for the Kinetic Robust KCenter Problem
, 2009
"... Two complications frequently arise in realworld applications, motion and the contamination of data by outliers. We consider a fundamental clustering problem, the kcenter problem, within the context of these two issues. We are given a finite point set S of size n and an integer k. In the standard k ..."
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Cited by 4 (3 self)
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Two complications frequently arise in realworld applications, motion and the contamination of data by outliers. We consider a fundamental clustering problem, the kcenter problem, within the context of these two issues. We are given a finite point set S of size n and an integer k. In the standard kcenter problem, the objective is to compute a set of k center points to minimize the maximum distance from any point of S to its closest center, or equivalently, the smallest radius such that S can be covered by k disks of this radius. In the discrete kcenter problem the disk centers are drawn from the points of S, and in the absolute kcenter problem the disk centers are unrestricted. We generalize this problem in two ways. First, we assume that points are in continuous motion, and the objective is to maintain a solution over time. Second, we assume that some given robustness parameter 0 < t ≤ 1 is given, and the objective is to compute the smallest radius such that there exist k disks of this radius that cover at least ⌈tn ⌉ points of S. We present a kinetic data structure (in the KDS framework) that maintains a (3 + ε)approximation for the robust discrete kcenter problem and a (4 + ε)approximation for the robust absolute kcenter problem, both under the assumption that k is a constant. We also improve on a previous 8approximation for the nonrobust discrete kinetic kcenter problem, for arbitrary k, and show that our data structure achieves a (4 + ε)approximation. All these results hold in any metric space of constant doubling dimension, which includes Euclidean space of constant dimension.
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 2 (1 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 significant impediment to approximation in many graph problems, such as kcenter, facility location, kmedian and the TSP. We demonstrate
Placement and Range Assignment in PowerAware Radio Networks
, 2007
"... Due to the extraordinary growth in the demand of mobile communication services in general, design of efficient systems for providing specialized services has also become an important issue in wireless mobility research. Broadly speaking, there are two major models for wireless networking: singleho ..."
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Cited by 1 (0 self)
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Due to the extraordinary growth in the demand of mobile communication services in general, design of efficient systems for providing specialized services has also become an important issue in wireless mobility research. Broadly speaking, there are two major models for wireless networking: singlehop and multihop. The single