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ALGORITHMICA
2002

Improved Algorithms for Uniform Partitions of Points

8 years 10 months ago
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...
Pankaj K. Agarwal, Binay K. Bhattacharya, Sandeep
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2002
Where ALGORITHMICA
Authors Pankaj K. Agarwal, Binay K. Bhattacharya, Sandeep Sen
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