An Efficient Algorithm for Transversal of Disjoint Convex Polygons

Abstract

Given a set S of n disjoint convex polygons {Pi | 1 ≤ i ≤ n} in a plane, each with ki vertices, the transversal problem is to determine whether there exists a straight line that goes through every polygon in S. We show that the transversal problem can be solved in O(N + n log n) time, where N=Σ= n i ki 1 is the total number of vertices of the polygons.