Output-sensitive algorithms for uniform partitions of points

Agarwal, Pankaj K. ; Bhattacharya, Binay K. ; Sen, Sandeep (1999) Output-sensitive algorithms for uniform partitions of points Lecture Notes in Computer Science, 1741 . pp. 403-414. ISSN 0302-9743

PDF - Author Version

Official URL: http://www.springerlink.com/content/026q6qd4n330le...

Related URL: http://dx.doi.org/10.1007/3-540-46632-0_41


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) + Δ points lies 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(b4Δ2 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 Δ. 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 Δ.

Item Type:Article
Source:Copyright of this article belongs to Springer.
ID Code:90081
Deposited On:04 May 2012 14:30
Last Modified:19 May 2016 04:25

Repository Staff Only: item control page