Optimal Bichromatic Plane Spanning Trees For Special Point Sets

Given a point set S=RꓴB, where R is a set of red points and B is a set of blue points, we desire to find T*, a minimum weight spanning tree such that every edge has one red endpoint and one blue endpoint and no two edges cross. We call T* a bichromatic plane minimum spanning tree (MinBPST). We say a point set is semi-collinear when the blue points lie on a line and the red points lie on one side of the line. In this thesis, we present an O(|B|^3|R|^2) running time algorithm for finding T* on a set of semi-collinear points. We also discuss an implementation of this algorithm. Additionally, we describe changes that can be made to the algorithm presented to solve other related problems. Finally, we describe properties of T* on semi-collinear point sets.