Enumerating the k best plane spanning trees

Abstract

A spanning tree constructed of straight line segments over a set of points in the Euclidean plane is called "non-crossing" or "plane tree", if no two segments intersect. Imposing the additional constraint of non-crossing segments makes many combinatorial geometric problems harder. In the case of plane spanning trees, however, we show that they can be enumerated efficiently in the order of their total length. This makes it possible to efficiently find the k best plane trees, or all those shorter than a given bound. © 2001 Elsevier Science B.V.