Connecting colored point sets Original Research Article

We study the following Ramsey-type problem. Let image be a two-colored set of n points in the plane. We show how to construct, in image time, a crossing-free spanning tree image for B, and a crossing-free spanning tree image for R, such that both the number of crossings between image and image and the diameters of image and image are kept small. The algorithm is conceptually simple and is implementable without using any non-trivial data structure. This improves over a previous method in Tokunaga [Intersection number of two connected geometric graphs, Inform. Process. Lett. 59 (1996) 331–333] that is less efficient in implementation and does not guarantee a diameter bound. Implicit to our approach is a new proof for the result in the reference above on the minimum number of crossings between image and image.