Computing the optimal bridge between two polygons

Abstract

Let P and Q be disjoint polygons in the plane. We consider the problem of finding an optimal bridge (p, q), P is an element of partial derivativeP and q is an element of partial derivativeQ, such that the length of the longest path from a point in P, passing through the bridge (p, q), to a point Q is minimized. We propose efficient algorithms for three cases according to whether P and Q are convex or not. These problems are motivated from the bridge construction between two islands (or the canal construction between two lakes).