## Finding Minimum Spanning Trees in O(m α(m,n)) Time (1999)

by
Seth Pettie

by
Seth Pettie

@TECHREPORT{Pettie99findingminimum,

author = {Seth Pettie},

title = {Finding Minimum Spanning Trees in O(m α(m,n)) Time},

institution = {},

year = {1999}

}

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.

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