On optimal bridges between two convex regions

Given k disjoint regions in the plane or space, the bridge problem asks for k − 1 line segments (optimal bridges) which connect these regions so as to minimize the length of the longest path between two points in the final connected region. We present O(n) and O(n2) time algorithms for finding an optimal bridge between two convex regions in the plane and space, respectively. An important property that the optimal configurations (i.e., the regions where candidate bridges can appear) are disjoint is shown in terms of the furthest-site Voronoi diagram. Our algorithms are simple and easy to be implemented.  2000 Elsevier Science B.V. All rights reserved.