Improved Algorithms for Uniform Partitions of Points

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 lie 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 O(b4( 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 . The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required (n2) time in the worst case even for constant values of b and . We also present a subquadratic algorithm for the special case of the two-dimensional problem when b = 2. Key Words. Bucketing, Hashing, Ra...

• Type: Journal
• Year: 2002
• Where: ALGORITHMICA
• Authors: Pankaj K. Agarwal, Binay K. Bhattacharya, Sandeep Sen
• Keywords: Algorithm, ALGORITHMICA 2002, Bucket, Two-dimensional Bucketing Problems