Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#235444] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Bhattacharya, BK; Sen, S, Improved algorithms for uniform partitions of points, Algorithmica (New York), vol. 32 no. 4 (2002), pp. 521-539
    (last updated on 2017/12/15)

    We consider the following one- and two-dimensional bucketing problems: Given a set 5 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 lie 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(b4(Δ2 + logn) + n). For the two-dimensional problem, we present a Monte Carlo algorithm that runs in subquadratic time for small 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. We also present a subquadratic algorithm for the special case of the two-dimensional problem when b = 2.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320