Computing the Optimal Bridge Between Two Convex Polygons

Abstract 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 , Q . We also present a very simple linear time constant factor approximate solution for this problem.