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## Incremental Clustering and Dynamic Information Retrieval (1997)

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Citations: | 191 - 4 self |

### Citations

14076 |
Computers and Intractability - A Guide to the Theory of NP-Completeness. W.H.Freeman&Co
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Citation Context ...k in Static Clustering. The closely-related problems of clustering to minimize diameter and radius are also called pairwise clustering and the k-center problem, respectively [2, 21]. Both are NP-hard =-=[17, 28]-=-, and in fact hard to approximate to within factor 2 for arbitrary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy [3], but in higher dimensions it is NP-hard to approximat... |

4843 |
Pattern Classification and Scene Analysis
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Citation Context ...lly, clustering is used to accelerate query processing by considering only a small number of representatives of the clusters, rather than the entire corpus. In addition, it is used for classification =-=[11]-=- and has been suggested as a method for facilitating browsing [9, 10]. The current information explosion, fueled by the availability of hypermedia and the World-wide Web, has led to the generation of ... |

4018 |
An Introduction to Modern Information Retrieval
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Citation Context ...ons [1, 20, 29, 35, 44]. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely related documents =-=[21, 24, 37, 44, 45, 47, 48]-=-. For this purpose, a distance metric is imposed over documents, enabling us to view them as points in a metric space. The central role of clustering in this application is captured by the so-called c... |

2797 |
Algorithms for clustering data
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Citation Context ...ber of clusters. Before describing our results in any greater detail, we motivate and formalize our new model. Clustering is used for data analysis and classification in a wide variety of application =-=[1, 12, 20, 27, 34]-=-. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely-related documents [13, 16, 34, 35, 37, 38... |

2250 |
A K-means clustering algorithm
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Citation Context ...ber of clusters. Before describing our results in any greater detail, we motivate and formalize our new model. Clustering is used for data analysis and classification in a wide variety of application =-=[1, 12, 20, 27, 34]-=-. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely-related documents [13, 16, 34, 35, 37, 38... |

979 | Managing Gigabytes: Compressing and indexing documents and images - Witten, Moffat, et al. - 1999 |

814 |
Cluster Analysis,
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Citation Context ...ber of clusters. Before describing our results in any greater detail, we motivate and formalize our new model. Clustering is used for data analysis and classification in a wide variety of application =-=[1, 12, 20, 27, 34]-=-. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely-related documents [13, 16, 34, 35, 37, 38... |

799 |
Automatic text processing.
- Salton
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Citation Context ...ion [1, 12, 20, 27, 34]. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely-related documents =-=[13, 16, 34, 35, 37, 38]-=-. For this purpose, a distance metric is imposed over documents, enabling us to view them as points in a metric space. The central role of clustering in this application is captured by the so-called c... |

777 | Scatter/gather: A cluster-based approach to browsing large document collections.
- Cutting, Karger, et al.
- 1992
(Show Context)
Citation Context ...ing only a small number of representatives of the clusters, rather than the entire corpus. In addition, it is used for classification [11] and has been suggested as a method for facilitating browsing =-=[9, 10]-=-. The current information explosion, fueled by the availability of hypermedia and the World-wide Web, has led to the generation of an ever-increasing volume of data, posing a growing challenge for inf... |

426 |
Cluster analysis.
- Aldenderfer, Blashfield
- 1984
(Show Context)
Citation Context ...ndation, Shell Foundation, and Xerox Corporation. 1417s1418 M. CHARIKAR, C. CHEKURI, T. FEDER, AND R. MOTWANI Clustering is used for data analysis and classification in a wide variety of applications =-=[1, 20, 29, 35, 44]-=-. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely related documents [21, 24, 37, 44, 45, 47... |

371 |
Clustering to minimize the maximum intercluster distance.
- GONZALEZ
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(Show Context)
Citation Context ...rary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy [3], but in higher dimensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used =-=[14, 15, 19, 29, 30]-=-. The furthest point heuristic due to Gonzalez [19] (see also Hochbaum and Shmoys [23, 24]) gives a 2-approximation in all metric spaces. This algorithm requires O(kn) distance computations, and when ... |

370 | Approximation Algorithms for Metric Facility Location and K-Median Problems Using the Primal-Dual Schema and Lagrangian Relaxation,”
- Jain, Vazirani
- 2001
(Show Context)
Citation Context ... to the minimum diameter and radius measures described above, several other objective functions have also been considered in the literature. A lot of recent work has focused on the k-median objective =-=[11, 36, 2]-=-. Here the goal is to assign points to k centers such that the sum of distances of points to their centers is minimized. Other objectives that have been studied include the objective of minimizing the... |

305 |
Rijsbergen, Information Retrieval
- Van
- 1979
(Show Context)
Citation Context ...ons [1, 20, 29, 35, 44]. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely related documents =-=[21, 24, 37, 44, 45, 47, 48]-=-. For this purpose, a distance metric is imposed over documents, enabling us to view them as points in a metric space. The central role of clustering in this application is captured by the so-called c... |

300 | Local search heuristics for k-median and facility location problems.
- Arya, Garg, et al.
- 2001
(Show Context)
Citation Context ... to the minimum diameter and radius measures described above, several other objective functions have also been considered in the literature. A lot of recent work has focused on the k-median objective =-=[11, 36, 2]-=-. Here the goal is to assign points to k centers such that the sum of distances of points to their centers is minimized. Other objectives that have been studied include the objective of minimizing the... |

295 | Clustering data streams
- Guha, Mishra, et al.
- 2000
(Show Context)
Citation Context ...nimize the maximum diameter or radius of the clusters produced. Subsequent to this work, other clustering objectives have also been studied in the streaming model, most notably the k-median objective =-=[28, 13]-=- and the sum of cluster diameters objective [14]. 2. Greedy algorithms. We begin by examining some natural greedy algorithms. A greedy incremental clustering algorithm always merges clusters to minimi... |

279 |
An algorithmic approach to network location problems, part ii: the p-medians,
- Kariv, Hakimi
- 1979
(Show Context)
Citation Context ...k in Static Clustering. The closely-related problems of clustering to minimize diameter and radius are also called pairwise clustering and the k-center problem, respectively [2, 21]. Both are NP-hard =-=[17, 28]-=-, and in fact hard to approximate to within factor 2 for arbitrary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy [3], but in higher dimensions it is NP-hard to approximat... |

252 |
A best possible heuristic for the k-center problem
- Hochbaum, Shmoys
- 1985
(Show Context)
Citation Context ...mensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used [14, 15, 19, 29, 30]. The furthest point heuristic due to Gonzalez [19] (see also Hochbaum and Shmoys =-=[23, 24]-=-) gives a 2-approximation in all metric spaces. This algorithm requires O(kn) distance computations, and when the metric space is induced by shortest-path distances in weighted graphs, the running tim... |

249 | Approximation schemes for covering and packing problems in image processing and VLSI,”
- Hochbaum, Maass
- 1985
(Show Context)
Citation Context ... , cover each point with a unit ball in ! d as it arrives, so as to minimize the total number of balls used. In the static case this problem is NP-Complete and there is a PTAS for any fixed dimension =-=[22]-=-. We note that in general metric spaces, it is not possible to achieve any bounded ratio. Our algorithm's analysis is based on a theorem from combinatorial geometry called Roger's theorem [36] (see al... |

249 | A constant-factor approximation algorithm for the k-median problem
- Charikar, Guha, et al.
- 1999
(Show Context)
Citation Context ... to the minimum diameter and radius measures described above, several other objective functions have also been considered in the literature. A lot of recent work has focused on the k-median objective =-=[11, 36, 2]-=-. Here the goal is to assign points to k centers such that the sum of distances of points to their centers is minimized. Other objectives that have been studied include the objective of minimizing the... |

246 |
Recent trends in hierarchical document clustering: A critical review”.
- Willett
- 1988
(Show Context)
Citation Context ...e propose the model described below. Hierarchical Agglomerative Clustering. The clustering strategy employed almost universally in information retrieval is Hierarchical Agglomerative Clustering (HAC) =-=[12, 34, 35, 37, 38, 39]-=-. This is also popular in other applications such as biology, medicine, image processing, and geographical information systems. The basic idea is: initially assign the n input points to n distinct clu... |

238 |
Introduction to modern information retrieval. McGraw-Hill Computer Science Series.
- Salton, McGill
- 1983
(Show Context)
Citation Context ...ion [1, 12, 20, 27, 34]. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely-related documents =-=[13, 16, 34, 35, 37, 38]-=-. For this purpose, a distance metric is imposed over documents, enabling us to view them as points in a metric space. The central role of clustering in this application is captured by the so-called c... |

188 |
Optimal algorithms for approximate clustering
- Feder, Greene
- 1988
(Show Context)
Citation Context ...rary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy [3], but in higher dimensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used =-=[14, 15, 19, 29, 30]-=-. The furthest point heuristic due to Gonzalez [19] (see also Hochbaum and Shmoys [23, 24]) gives a 2-approximation in all metric spaces. This algorithm requires O(kn) distance computations, and when ... |

183 | Combinatorial Geometry
- Pach, Agarwal
- 1995
(Show Context)
Citation Context ...n general metric spaces, it is not possible to achieve any bounded ratio. Our algorithm's analysis is based on a theorem from combinatorial geometry called Roger's theorem [36] (see also Theorem 7.17 =-=[33]-=-), which says that R d can be covered by any convex shape with covering density O(d log d). Since the volume of a radius 2 ball is 2 d times the volume of a unitradius ball, the number of balls needed... |

158 | The use of hierarchical clustering in information retrieval, - Jardine, Rijsbergen - 1971 |

152 |
Packing and Covering
- Rogers
- 1964
(Show Context)
Citation Context ...mension [22]. We note that in general metric spaces, it is not possible to achieve any bounded ratio. Our algorithm's analysis is based on a theorem from combinatorial geometry called Roger's theorem =-=[36]-=- (see also Theorem 7.17 [33]), which says that R d can be covered by any convex shape with covering density O(d log d). Since the volume of a radius 2 ball is 2 d times the volume of a unitradius ball... |

146 |
Optimal packing and covering in the plane are NP-complete .
- Fowler, Paterson, et al.
- 1981
(Show Context)
Citation Context ...rary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy [3], but in higher dimensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used =-=[14, 15, 19, 29, 30]-=-. The furthest point heuristic due to Gonzalez [19] (see also Hochbaum and Shmoys [23, 24]) gives a 2-approximation in all metric spaces. This algorithm requires O(kn) distance computations, and when ... |

140 | On the complexity of some common geometric location problems,”
- Megiddo, Supowit
- 1984
(Show Context)
Citation Context ...420 M. CHARIKAR, C. CHEKURI, T. FEDER, AND R. MOTWANI tering on the line is easy [6], but in higher dimensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used =-=[22, 23, 27, 39, 40]-=-. The furthest point heuristic due to Gonzalez [27] (see also Hochbaum and Shmoys [32, 33]) gives a 2-approximation in all metric spaces. This algorithm requires O(kn) distance computations, and when ... |

135 | Constant interaction-time Scatter/Gather browsing of very large document collections.
- Cutting, Karger, et al.
- 1993
(Show Context)
Citation Context ...ing only a small number of representatives of the clusters, rather than the entire corpus. In addition, it is used for classification [11] and has been suggested as a method for facilitating browsing =-=[9, 10]-=-. The current information explosion, fueled by the availability of hypermedia and the World-wide Web, has led to the generation of an ever-increasing volume of data, posing a growing challenge for inf... |

128 | Theorie der konvexen Körper - Bonnesen, Fenchel - 1974 |

115 |
A unified approach to approximation algorithms for bottleneck problems,
- Hochbaum, Shmoys
- 1986
(Show Context)
Citation Context ...mensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used [14, 15, 19, 29, 30]. The furthest point heuristic due to Gonzalez [19] (see also Hochbaum and Shmoys =-=[23, 24]-=-) gives a 2-approximation in all metric spaces. This algorithm requires O(kn) distance computations, and when the metric space is induced by shortest-path distances in weighted graphs, the running tim... |

102 | A survey of information retrieval and filtering methods.
- Faloutsos, Oard
- 1995
(Show Context)
Citation Context ...ion [1, 12, 20, 27, 34]. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely-related documents =-=[13, 16, 34, 35, 37, 38]-=-. For this purpose, a distance metric is imposed over documents, enabling us to view them as points in a metric space. The central role of clustering in this application is captured by the so-called c... |

94 | E.: Nonclairvoyant scheduling.
- Motwani, Phillips, et al.
- 1994
(Show Context)
Citation Context ...r from [1=e; 1] according to the probability density function 1=r, set d 1 to rx, and redefine fi = e and ff = e=(e\Gamma1). Similar randomization of doublingalgorithms was used earlier in scheduling =-=[31]-=-, and later in other applications [7, 18]. Theorem 9 The Randomized Doubling Algorithm has expected performance ratio 2es5:437 in any metric space. The same bound is also achieved for the radius measu... |

94 | Better streaming algorithms for clustering problems.
- Charikar, O’Callaghan, et al.
- 2003
(Show Context)
Citation Context ...nimize the maximum diameter or radius of the clusters produced. Subsequent to this work, other clustering objectives have also been studied in the streaming model, most notably the k-median objective =-=[28, 13]-=- and the sum of cluster diameters objective [14]. 2. Greedy algorithms. We begin by examining some natural greedy algorithms. A greedy incremental clustering algorithm always merges clusters to minimi... |

92 | Algorithms for facility location problems with outliers.
- Charikar, Khuller, et al.
- 2001
(Show Context)
Citation Context ... the sum of all distances within each cluster [3, 18] and that of minimizing the sum of cluster diameters [14]. In addition to this, outlier formulations of clustering problems have also been studied =-=[12]-=-. Here the algorithm is allowed to discard a fraction of the input as outliers and is required to obtain a clustering solution that minimizes a given objective function on the remaining input points. ... |

89 | An improved approximation ratio for the minimum latency problem,
- Goemans, Kleinberg
- 1998
(Show Context)
Citation Context ...bility density function 1=r, set d 1 to rx, and redefine fi = e and ff = e=(e\Gamma1). Similar randomization of doublingalgorithms was used earlier in scheduling [31], and later in other applications =-=[7, 18]-=-. Theorem 9 The Randomized Doubling Algorithm has expected performance ratio 2es5:437 in any metric space. The same bound is also achieved for the radius measure. Proof: Let oe be the sequence of upda... |

78 | Approximation algorithms for geometric problems. In Approximation Algorithms for NP-Hard Problems.
- BERN, EPPSTEIN
- 1996
(Show Context)
Citation Context ...eration here. Previous Work in Static Clustering. The closely-related problems of clustering to minimize diameter and radius are also called pairwise clustering and the k-center problem, respectively =-=[2, 21]-=-. Both are NP-hard [17, 28], and in fact hard to approximate to within factor 2 for arbitrary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy [3], but in higher dimensions ... |

66 | editors. Information Retrieval: Data Structures and Algorithms - Frakes, Baeza-Yates - 1992 |

65 |
Approximation schemes for clustering problems.
- Vega, Karpinski, et al.
- 2003
(Show Context)
Citation Context ...enters such that the sum of distances of points to their centers is minimized. Other objectives that have been studied include the objective of minimizing the sum of all distances within each cluster =-=[3, 18]-=- and that of minimizing the sum of cluster diameters [14]. In addition to this, outlier formulations of clustering problems have also been studied [12]. Here the algorithm is allowed to discard a frac... |

64 |
On the complexity of clustering problems,
- Brucker
- 1978
(Show Context)
Citation Context ... problem, respectively [2, 21]. Both are NP-hard [17, 28], and in fact hard to approximate to within factor 2 for arbitrary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy =-=[3]-=-, but in higher dimensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used [14, 15, 19, 29, 30]. The furthest point heuristic due to Gonzalez [19] (see also Ho... |

64 | Improved scheduling algorithms for minsum criteria.
- Chakrabarti, Phillips, et al.
- 1996
(Show Context)
Citation Context ...bility density function 1=r, set d 1 to rx, and redefine fi = e and ff = e=(e\Gamma1). Similar randomization of doublingalgorithms was used earlier in scheduling [31], and later in other applications =-=[7, 18]-=-. Theorem 9 The Randomized Doubling Algorithm has expected performance ratio 2es5:437 in any metric space. The same bound is also achieved for the radius measure. Proof: Let oe be the sequence of upda... |

63 |
Approximating min-sum k-clustering in Metric Spaces
- Bartal, Charikar, et al.
- 2001
(Show Context)
Citation Context ...enters such that the sum of distances of points to their centers is minimized. Other objectives that have been studied include the objective of minimizing the sum of all distances within each cluster =-=[3, 18]-=- and that of minimizing the sum of cluster diameters [14]. In addition to this, outlier formulations of clustering problems have also been studied [12]. Here the algorithm is allowed to discard a frac... |

62 |
Incremental Clustering for Dynamic Information Processing,”
- Can
- 1993
(Show Context)
Citation Context ...orithms are not suitable for maintaining clusters in such a dynamic environment, and they have been strugglingwith the problem of updating clusters without frequently performing complete reclustering =-=[4, 5, 6, 8, 35]-=-. From a theoretical perspective, many different formulations are possible for this dynamic clustering problem, and it is not clear a priori which of these best addresses the concerns of the practitio... |

45 |
Clustering Algorithms”, in Information Retrieval Data Structures and Algorithms,
- Rasmussen
- 1992
(Show Context)
Citation Context ...ndation, Shell Foundation, and Xerox Corporation. 1417s1418 M. CHARIKAR, C. CHEKURI, T. FEDER, AND R. MOTWANI Clustering is used for data analysis and classification in a wide variety of applications =-=[1, 20, 29, 35, 44]-=-. It has proved to be a particularly important tool in information retrieval for constructing a taxonomy of a corpus of documents by forming groups of closely related documents [21, 24, 37, 44, 45, 47... |

40 | Clustering to minimize the sum of cluster diameters.
- Charikar, Panigrahy
- 2004
(Show Context)
Citation Context ...ters is minimized. Other objectives that have been studied include the objective of minimizing the sum of all distances within each cluster [3, 18] and that of minimizing the sum of cluster diameters =-=[14]-=-. In addition to this, outlier formulations of clustering problems have also been studied [12]. Here the algorithm is allowed to discard a fraction of the input as outliers and is required to obtain a... |

26 | Postcolonial computing”,
- Irani, Dourish, et al.
- 2010
(Show Context)
Citation Context ...age, while cluster representatives are preserved in main memory [32]. We have avoided labeling this model as the online clustering problem or referring to the performance ratio as a competitive ratio =-=[25]-=- for the following reasons. Recall that in an online setting, we would compare the performance of an algorithm to that of an adversary which knows the update sequence in advance but must process the p... |

23 |
Various notions of approximations:
- Hochbaum
- 1997
(Show Context)
Citation Context ...eration here. Previous Work in Static Clustering. The closely-related problems of clustering to minimize diameter and radius are also called pairwise clustering and the k-center problem, respectively =-=[2, 21]-=-. Both are NP-hard [17, 28], and in fact hard to approximate to within factor 2 for arbitrary metric spaces [2, 21]. For Euclidean spaces, clustering on the line is easy [3], but in higher dimensions ... |

21 |
Online computation. In Approximation Algorithms for NP-hard Problems
- Irani, Karlin
- 1996
(Show Context)
Citation Context ...age, while cluster representatives are preserved in main memory [42]. We have avoided labeling this model as the online clustering problem or referring to the performance ratio as a competitive ratio =-=[34]-=- for the following reasons. Recall that in an online setting, we would compare the performance of an algorithm to that of an adversary which knows the update sequence in advance but must process the p... |

7 |
Clustering Algorithms. Chapter 16
- Rasmussen
- 1992
(Show Context)
Citation Context |

7 |
Non-clairvoyant scheduling, Theoret
- Motwani, Torng
- 1994
(Show Context)
Citation Context ...alue r from [1/e, 1] according to the probability density function 1/r, set d1 to rx, and redefine β = e and α = e/(e − 1). Similar randomization of doubling algorithms was used earlier in scheduling =-=[41]-=-, and later in other applications [10, 26]. Theorem 3.8. The randomized doubling algorithm has expected performance ratio 2e ≈ 5.437 in any metric space. The same bound is also achieved for the radius... |

6 |
A Dynamic Cluster Maintenance System for Information Retrieval
- Can, Ozkarahan, et al.
- 1987
(Show Context)
Citation Context ...orithms are not suitable for maintaining clusters in such a dynamic environment, and they have been strugglingwith the problem of updating clusters without frequently performing complete reclustering =-=[4, 5, 6, 8, 35]-=-. From a theoretical perspective, many different formulations are possible for this dynamic clustering problem, and it is not clear a priori which of these best addresses the concerns of the practitio... |

5 |
On the complexity of some common geometric problems
- Megiddo, Supowit
- 1984
(Show Context)
Citation Context |

4 |
Incremental Clustering for Dynamic Document Databases
- Can, Drochak
- 1990
(Show Context)
Citation Context ...orithms are not suitable for maintaining clusters in such a dynamic environment, and they have been strugglingwith the problem of updating clusters without frequently performing complete reclustering =-=[4, 5, 6, 8, 35]-=-. From a theoretical perspective, many different formulations are possible for this dynamic clustering problem, and it is not clear a priori which of these best addresses the concerns of the practitio... |

4 | A best possible heuristic for the -center problem - Hochbaum, Shmoys - 1985 |

3 |
A Global Approach to Record Clustering and File Organization
- Omiecinski, Scheuermann
- 1984
(Show Context)
Citation Context ...been observed that such incremental algorithms exhibit good paging performance when the clusters themselves are stored in secondary storage, while cluster representatives are preserved in main memory =-=[32]-=-. We have avoided labeling this model as the online clustering problem or referring to the performance ratio as a competitive ratio [25] for the following reasons. Recall that in an online setting, we... |

3 | Pattern Class@cation and Scene Analysis - Duda, Hart - 1973 |

2 |
Dynamic clustering for time incremental data
- Chaudhri
- 1994
(Show Context)
Citation Context |

2 |
Managing Gigabytes: Compressingand Indexing Documents and Images
- Witten, Moffat, et al.
- 1994
(Show Context)
Citation Context ...and the World-wide Web, has led to the generation of an ever-increasing volume of data, posing a growing challenge for information retrieval systems to efficiently store and retrieve this information =-=[40]-=-. A major issue that document databases are now facing is the extremely high rate of update. Several practitioners have complained that existing clustering algorithms are not suitable for maintaining ... |

2 |
Drochak II. Incremental clustering for dynamic document databases
- Can, D
- 1990
(Show Context)
Citation Context ...rithms are not suitable for maintaining clusters in such a dynamic environment, and they have been struggling with the problem of updating clusters without frequently performing complete reclustering =-=[7, 8, 9, 15, 45]-=-. From a theoretical perspective, many different formulations are possible for this dynamic clustering problem, and it is not clear a priori which of these best addresses the concerns of the practitio... |

1 |
Baeza-Yates, editors. Information Retrieval: Data Structures and Algorithms
- FrakesandR
- 1992
(Show Context)
Citation Context |

1 |
bounds on metric k-center problems
- Lower
- 1988
(Show Context)
Citation Context |

1 |
Lower bounds on metric k-center problems
- Mentzer
- 1988
(Show Context)
Citation Context ...420 M. CHARIKAR, C. CHEKURI, T. FEDER, AND R. MOTWANI tering on the line is easy [6], but in higher dimensions it is NP-hard to approximate to within factors close to 2, regardless of the metric used =-=[22, 23, 27, 39, 40]-=-. The furthest point heuristic due to Gonzalez [27] (see also Hochbaum and Shmoys [32, 33]) gives a 2-approximation in all metric spaces. This algorithm requires O(kn) distance computations, and when ... |

1 | Various Notions of Approximations - Hoehbaum - 1996 |

1 | The Use of Hierarchical Clusteringin Information Retrieval - Rijsbergen - 1971 |

1 | bounds on metric -center problems - Lower - 1988 |