Sollin Minimum Spanning Tree

Colors: Red: Arcs in the minimum spanning forest/tree

This algorithm keeps a forest of minimum spanning trees which it continuously connects via the least cost arc leaving each tree. To begin each node is made its own minimum spanning tree. From here the shortest arc leaving each tree (which doesn't connect to a node already belonging to the current tree) is added along the minimum spanning tree it connects to. This continues until there exists a single spanning tree of the entire graph. This functions in O(m log n).

Although rediscovered by Sollin in the 1960's, this algorithm was originally discovered by Czech mathematician Otakar Boruvka. A definite pioneer, Boruvka did extensive work in graph theory long before this was an established mathematical discipline. He was born in Uhersky Ostroh, in what is today the Czech Republic and attended grammar school before moving in 1916 to a military school which lead to his entrance in the military technical academy in Modling near Vienna. His 1926 paper O jistem problemu minimalnim (On a certain minimal problem) described his algorithm for finding the minimum spanning tree of an electrical network.