Abstract
Given nonintersecting simple polygonsP andQ, two verticespeP andqe Q are said to be visible if\(\overline {pq}\) does not properly intersectP orQ. We present a parallel algorithm for finding a closest pair among all visible pairs (p,q),peP andqeQ. The algorithm runs in time O(logn) using O(n) processors on a CREW PRAM, wheren=¦P¦+¦Q¦. This algorithm can be implemented serially in Θ(n) time, which gives a new optimal sequential solution for this problem.
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