A minimum spanning tree algorithm with inverse-Ackermann type complexity
Bernard Chazelle · Journal of the ACM · 2000
A deterministic algorithm for computing a minimum spanning tree of a connected graph is presented. Its running time is 0 ( 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.