Computing the Optimal Bridge between Two Polygons

Let P and Q be disjoint polygons in the plane. We consider the problem of finding an optimal bridge (p,q) , p∈ \partial P and q∈ \partial Q , 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).