Efficient algorithms for computing the maximum distance between two finite planar sets

Abstract

An 0( n log n) algorithm is presented for computing the maximum euclidean distance between two finite planar sets of n points. When the n points form the vertices of simple polygons this complexity can be reduced to 0( n). The algorithm is empirically compared to the brute-force method as well as an alternate 0( n 2) algorithm. Both the 0( n log n) and 0( n 2) algorithms run in 0( n) expected time for many underlying distributions of the points. An ϵ-approximate algorithm can be obtained that runs in 0(n + 1 ϵ ) worst-case time.