# Output-sensitive algorithms for uniform partitions of points

Published

Conference Paper

© Springer-Verlag Berlin Heidelberg 1999. We consider the following one- and two-dimensional bucketing problems: Given a set S of n points in ℝ1 or ℝ2 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) + △ points lies in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and △. No prior knowledge of △ is necessary for our algorithms. For the one-dimensional problem, we give a deterministic algorithm that achieves a running time of 0(b4△2 log n + n). For the two-dimensional problem, we present a Monte-Carlo algorithm that runs in sub-quadratic time for certain values of b and △. The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required Ω(n2) time in the worst case even for constant values of b and △.

### Full Text

### Duke Authors

### Cited Authors

- Agarwal, PK; Bhattacharya, BK; Sen, S

### Published Date

- January 1, 1999

### Published In

### Volume / Issue

- 1741 /

### Start / End Page

- 403 - 414

### Electronic International Standard Serial Number (EISSN)

- 1611-3349

### International Standard Serial Number (ISSN)

- 0302-9743

### International Standard Book Number 10 (ISBN-10)

- 3540669167

### International Standard Book Number 13 (ISBN-13)

- 9783540669166

### Digital Object Identifier (DOI)

- 10.1007/3-540-46632-0_41

### Citation Source

- Scopus