Finding Minimum Spanning Trees in O(m α(m,n)) Time
Department of Computer Sciences; The University of Texas at Austin
Austin, TX 78712
We describe a deterministic minimum spanning tree algorithm running in time O(m α(m; n)), where α is a natural inverse of Ackermann's function and m and n are the number of edges and vertices, respectively. This improves upon the O(m α(m; n) log α(m; n)) bound established by Chazelle in 1997. A similar O(m α(m; n))-time algorithm was discovered independently by Chazelle, predating the algorithm presented here by many months. This paper may still be of interest for its alternative exposition.