DETERMINING THE SEPARATION OF SIMPLE POLYGONS

Abstract

Given simple polygons P and Q, their separation, denoted by σ(P, Q), is defined to be the minimum distance between their boundaries. We present a parallel algorithm for finding a closest pair among all pairs (p, q), p ∈ P and q ∈ Q. The algorithm runs in O ( log n) time using O(n) processors on a CREW PRAM, where n = |P| + |Q|. This algorithm is time-optimal and improves by a factor of O ( log n) on the time complexity of previous parallel methods. The algorithm can be implemented serially in Θ (n) time, which gives the first optimal sequential algorithm for determining the separation of simple polygons. Our results are obtained by providing a unified treatment of the separation and the closest visible vertex problems for simple polygons.