A minimum spanning tree algorithm with inverse-ackermann type complexity

Abstract

A deterministic algorithm for computing a minimum spanning tree of a connected graph is presented. Its running time is O(m α (m, n)), where α is the classical functional inverse of Ackermann's function and n (respectively, m) is the number of vertices (respectively, edges). The algorithm is comparison-based: it uses pointers, not arrays, and it makes no numeric assumptions on the edge costs. © 2000 ACM.