Agarwal, P. K. ; Bhattacharya, B. K. ; Sen, S.
(2002)
*Improved algorithms for uniform partitions of points*
Algorithmica, 32
(4).
pp. 521-539.
ISSN 0178-4617

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Official URL: http://www.springerlink.com/content/f7f3fm3b87pbke...

Related URL: http://dx.doi.org/10.1007/s00453-001-0084-9

## Abstract

We consider the following one- and two-dimensional bucketing problems: Given a set S of n points in R^{1} or R^{2} and a positive integer b , distribute the points of S into b equal-size buckets so that the maximum number of points in a bucket is minimized. Suppose at most (n/b)+Δ points lie in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and Δ. No prior knowledge of Δ is necessary for our algorithms. For the one-dimensional problem, we give a deterministic algorithm that achieves a running time of O(b^{4}(Δ^{2}+log n)+n) . For the two-dimensional problem, we present a Monte Carlo algorithm that runs in subquadratic time for small values of b and Δ. The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required Ω(n^{2}) time in the worst case even for constant values of b and Δ. We also present a subquadratic algorithm for the special case of the two-dimensional problem when b=2.

Item Type: | Article |
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Source: | Copyright of this article belongs to Springer. |

Keywords: | Bucketing; Hashing; Random Sampling; Arrangements |

ID Code: | 53434 |

Deposited On: | 08 Aug 2011 12:09 |

Last Modified: | 08 Aug 2011 12:09 |

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