Home > Boruvka's algorithm
Trees (structure)Boruvka's algorithm is an algorithm for finding minimum spanning trees. It was first published in 1926 by Otakar Boruvka as a method of efficiently electrifying Bohemia.
Boruvka's algorithm, in pseudocode, given a graph G, is:
- Copy the vertices of G into a new graph, L, with no edges.
- While L is not connected (that is, it is a forest of more than one tree):
- For each tree T in L, find the smallest edge in G connecting a vertex in T to one outside it.
- Add that edge to L, reducing the number of trees in L by one.
Boruvka's algorithm can be shown to run in time O(Elog V), where E is the number of edges, and V is the number of vertices in G.
Other algorithms for this problem include Prim's algorithm and Kruskal's algorithm. Faster algorithms can be obtained by combining Prim's algorithm with Boruvka's. A faster randomized version of Boruvka's algorithm due to Karger, Klein, and Tarjan runs in expected time. The best known minimum spanning tree algorithm by Bernard Chazelle is based on Boruvka's and runs in O(E α(V)) time, where α is the inverse of the Ackermann function.
Graph algorithms
Optimization algorithms
