A Faster Convex-Hull Algorithm via Bucketing

In the convex-hull problem, in two-dimensional space, the task is to find, for a given sequence S of n points, the smallest convex polygon for which each point of S is either in its interior or on its boundary. In this paper, we propose a variant of the classical bucketing algorithm that (1) solves the convex-hull problem for any multiset of points, (2) uses O(n−−√) words of extra space, (3) runs in O(n) expected time on points drawn independently and uniformly from a rectangle, and (4) requires O(nlgn) time in the worst case. Also, we perform experiments to compare bucketing to other alternatives that are known to work in linear expected time. In our tests, in the integer-coordinate setting, bucketing was a clear winner compared to the considered competitors (plane-sweep, divide & conquer, quickhull, and throw-away).