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## Algorithms for dynamic geometric problems over data streams (2004)

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Venue: | In STOC ’04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing |

Citations: | 44 - 6 self |

### Citations

845 | The space complexity of approximating the frequency moments
- Alon, Matias, et al.
- 1999
(Show Context)
Citation Context ...gorithm design. The initial research in streaming algorithms has focused on computing simple numerical statistics of the input, like median [23], number of distinct elements [11] or frequency moments =-=[1]-=-. More recently, the researchers showed that one can use those algorithms as subroutines to solve more complex problems (e.g., cf. [13]); see the survey [24] for detailed description of the past and r... |

444 | Probabilistic counting algorithms for data base applications
- Flajolet, Martin
- 1985
(Show Context)
Citation Context ... exciting challenge for algorithm design. The initial research in streaming algorithms has focused on computing simple numerical statistics of the input, like median [23], number of distinct elements =-=[11]-=- or frequency moments [1]. More recently, the researchers showed that one can use those algorithms as subroutines to solve more complex problems (e.g., cf. [13]); see the survey [24] for detailed desc... |

413 | An improved data stream summary: The count-min sketch and its applications - Cormode, Muthukrishnan |

351 | Probabilistic approximation of metric spaces and its algorithmic applications.
- Bartal
- 1996
(Show Context)
Citation Context ...the consecutive edges decrease by at least a certain factor k ? 1. An HST (with parameter k) is the metric space with the leaves of T as points and with the shortest-path metrics over T . Building on =-=[3]-=-, Charikar et al [5] showed the following Fact 1. Let P be a set of points from f1 : : : \Delta g d . Then the metric over P induced by the lp norm can be embedded into a convex combination of dominat... |

324 | Stable distributions, pseudorandom generators, embeddings and data stream computation. - Indyk - 2000 |

300 | Local search heuristics for k-median and facility location problems. - Arya, Garg, et al. - 2001 |

295 | Clustering data streams - Guha, Mishra, et al. - 2000 |

214 | Efficient search for approximate nearest neighbor in high dimensional spaces
- Kushilevitz, Ostrovsky, et al.
- 2000
(Show Context)
Citation Context ...the number of odd values of n(c) (we call it Odd-Count) was not investigated earlier in the literature. We show how to solve it by adapting a method for dimensionality reduction in a hypercube due to =-=[20]-=-. The next problem (that we call BoundedCount) was not addressed in the literature either, although it generalizes the problem of counting the non-zero entries (for T = 1) or counting the number of el... |

138 | Selection and sorting with limited storage. - Munro, Paterson - 1980 |

115 | An analysis of the greedy algorithm for the submodular set covering problem - Wolsey - 1982 |

107 | small-space algorithms for approximate histogram maintenance. STOC - Fast - 2002 |

94 | Better streaming algorithms for clustering problems. - Charikar, O’Callaghan, et al. - 2003 |

71 | Online facility location. - Meyerson - 2001 |

49 | Approximating the minimum spanning tree weight in sublinear time - Chazelle, Rubinfeld, et al. - 2001 |

22 | Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time. - Czumaj, Sohler - 2009 |

20 |
Comparing data streams using hamming norms
- Cormode, Datar, et al.
- 2002
(Show Context)
Citation Context ...vector nB \GammasnR, a problem that has been solved in [18]. Estimating of the number of c's such that nP (c) ? 0 is equivalent to maintaining the number of distinct elements in a stream [11, 1] (see =-=[8]-=- for a more recent description of that algorithm). The problem of estimating the number of odd values of n(c) (we call it Odd-Count) was not investigated earlier in the literature. We show how to solv... |

19 | Data streams: Algorithm and applications (invited talk at soda’03). available at http://athos.rutgers.edu - Muthukrishnan - 2003 |

16 | The Sensor Spectrum: Technology, Trends, and Requirements”, - Hellerstein, Hong, et al. - 2003 |

13 | Similarity estimation techniques from rounding - Charikar - 2002 |

12 |
Fast color image retrieval via embeddings.
- Indyk, Thaper
- 2003
(Show Context)
Citation Context ...), it is likely that in practice the actual quality of the reported answers will be much better. In particular, the experimental evaluation of a variant of the algorithm for the bi-chromatic matching =-=[19]-=- shows that the estimation provided by the algorithm is, for natural data sets, within 10% of the actual value. We also mention that the approximation factor for facility location can be improved to O... |

8 | Coresets for k-means and k-medians and their applications - Har-Peled, Mazumdar - 2004 |

2 | Location streams: Models and algorithms - Hoffman, Muthukrishnan, et al. - 2004 |

1 |
Estimating the weight of euclidean minimum spanning trees in data streams
- Frahling, Sohler
- 2004
(Show Context)
Citation Context ...nsidered earlier in the metric setting [21]. However, the algorithms developed in that paper were using \Omega (jF j) space, which is linear in n in the worst case. Very recently, Frahling and Sohler =-=[12]-=- (building on the techniques of [7, 10]) gave an algorithm for (1+ffl)-approximation of the MST cost in the insertions-only model. 4 We mention that the idea of using greedy algorithms in the data str... |

1 | Approximating a finite metricby a small number of tree metrics - Charikar, Chekuri, et al. - 1998 |

1 | Probabilisticcounting algorithms for data base applications - Flajolet, Martin - 1985 |