On a proposed divide-and-conquer minimal spanning tree algorithm

Abstract

In a recent paper published in this journal, R. Chang and R. Lee purport to devise an O(N log N) time minimal spanning tree algorithm for N points in the plane that is based on a divide-and-conquer strategy using Voronoi diagrams. In this brief note, we present families of problem instances to show that the Chang-Lee worst-case timing analysis is incorrect, resulting in a time bound of O(N2 log N). Since it is known that alternate, truly O(N log N) time algorithms are available anyway, the general utility of the Chang-Lee algorithm is questionable. © 1988 BIT Foundations.