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Output-Sensitive Algorithms for Uniform Partitions of Points

  • Pankaj K. Agarwal
  • Binay K. Bhattacharya
  • Sandeep Sen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

We consider the following one- and two-dimensional bucke- ting 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 pre- sent 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 4Δ2 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 Ή(n 2) time in the worst case even for constant values of b and Δ.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Pankaj K. Agarwal
    • 1
  • Binay K. Bhattacharya
    • 2
  • Sandeep Sen
    • 3
  1. 1.Center for Geometric Computing, Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  3. 3.Department of Computer Science and EngineeringIIT DelhiNew DelhiIndia

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