Computing the optimal bridge between two convex polygons

We present an efficient algorithm for solving the following problem. Given two disjoint convex polygonal regions P, Q in the plane, add a line segment to connect them so as to minimize the maximum of the distances between points in one region and points in the other region. An O(n(2) log n) time algorithm is presented to find such a line segment (optimal bridge) (p, q), where n is the maximal cardinality of P, e. We also present a very simple linear time constant factor approximate solution for this problem. (C) 1999 Elsevier Science B.V. All rights reserved.