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 eals¹ or eals² 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.