Agarwal, Pankaj K. ; Bhattacharya, Binay K. ; Sen, Sandeep (1999) Outputsensitive algorithms for uniform partitions of points Lecture Notes in Computer Science, 1741 . pp. 403414. ISSN 03029743

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Related URL: http://dx.doi.org/10.1007/3540466320_41
Abstract
We consider the following one and twodimensional bucketing problems: Given a set S of n points in R^{1} or R^{2} and a positive integer b, distribute the points of S into b equalsize 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 onedimensional problem, we give a deterministic algorithm that achieves a running time of O(b^{4}Δ^{2} log n + n). For the twodimensional problem, we present a MonteCarlo algorithm that runs in subquadratic time for certain values of b and Δ. The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required Ω(n^{2}) time in the worst case even for constant values of b and Δ.
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