What is boruvkas algorithm?

Boruvka's algorithm, also known as Sollin's algorithm, is a graph algorithm that finds the minimum spanning tree of a graph. It was invented by Otakar Boruvka in 1926.

The algorithm works by repeatedly adding to the minimum spanning tree the cheapest edge that connects two components until the graph is connected. Initially, each vertex is considered as a separate component. At each step, the algorithm finds the cheapest edge that connects a vertex in one component to a vertex in another component.

Boruvka's algorithm runs in O(E log V) time, where E is the number of edges and V is the number of vertices in the graph. This makes it a very fast algorithm for finding the minimum spanning tree of a large graph.

One disadvantage of Boruvka's algorithm is that it may produce a spanning tree with more edges than necessary in some cases, although the resulting tree will still have the same total weight as the minimum spanning tree.

Boruvka's algorithm has applications in network design, clustering, and image segmentation.