## Estimating the weight of metric minimum spanning trees in sublinear-time

Venue: | in Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC |

Citations: | 17 - 5 self |

### BibTeX

@INPROCEEDINGS{Czumaj_estimatingthe,

author = {Artur Czumaj and Christian Sohler},

title = {Estimating the weight of metric minimum spanning trees in sublinear-time},

booktitle = {in Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC},

year = {},

pages = {175--183}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we present a sublinear time (1+ ɛ)-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is Õ(n/ɛO(1)). Since the full description of an n-point metric space is of size Θ(n 2),the complexity of our algorithm is sublinear with respect to the input size. Our algorithm is almost optimal as it is not possible to approximate in o(n) time the weight of the minimum spanning tree to within any factor. Furthermore,it has been previously shown that no o(n 2) algorithm exists that returns a spanning tree whose weight is within a constant times the optimum.

### Citations

895 |
Approximation Algorithms
- Vazirani
- 2001
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424 | Property testing and its connection to learning and approximation
- Goldreich, Goldwasser, et al.
- 1998
(Show Context)
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240 | A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields - CALLAHAN, KOSARAJU - 1995 |

178 | Fast Monte-Carlo algorithms for finding low-rank approximations
- Frieze, Kannan, et al.
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139 | Spanning trees and spanners
- Eppstein
(Show Context)
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115 | A randomized linear-time algorithm to find minimum spanning trees
- Karger, Tarjan, et al.
- 1995
(Show Context)
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79 | Sublinear time algorithms for metric space problems
- Indyk
- 1999
(Show Context)
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74 |
A minimum spanning tree algorithm with inverse-Ackermann type complexity
- Chazelle
- 2000
(Show Context)
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72 |
The Regularity Lemma and approximation schemes for dense problems
- FRIEZE, KANNAN
- 1996
(Show Context)
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57 | Testing of clustering
- Alon, Dar, et al.
- 2003
(Show Context)
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46 | Sublinear time approximate clustering
- Mishra, Oblinger, et al.
- 2001
(Show Context)
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46 | An optimal minimum spanning tree algorithm - Pettie, Ramachandran |

41 | Approximating the minimum spanning tree weight in sublinear time
- Chazelle, Rubinfeld, et al.
- 2001
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- Indyk
- 1999
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37 | A sublinear algorithm for weakly approximating edit distance
- BATU, ERGÜN, et al.
- 2003
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2 | On Constructing minimum spanning trees in k-demensional spaces and related problems - Yao - 1982 |

1 |
Sublinear geometric algorithms
- Magen
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