Borůvka's algorithm

A procedure taken from Borůvka's algorithm is also used to reduce the size of the graph at each recursion.

It is radically different from the classical sequential problem, although the most basic approach resembles Borůvka's algorithm.

The worst case runtime is equivalent to the runtime of Borůvka's algorithm.

Today, this algorithm is known as Borůvka's algorithm.

Other algorithms for this problem include Kruskal's algorithm and Borůvka's algorithm.

Some bear similarities to Borůvka's algorithm for the classical MST problem.

Designating each vertex or set of connected vertices a "component", pseudocode for Borůvka's algorithm is:

They found a linear time randomized algorithm based on a combination of Borůvka's algorithm and the reverse-delete algorithm.

Borůvka's algorithm is an algorithm for finding a minimum spanning tree in a graph for which all edge weights are distinct.

Otakar Borůvka publishes Borůvka's algorithm, introducing the greedy algorithm.

The first algorithm for finding a minimum spanning tree was developed by Czech scientist Otakar Borůvka in 1926 (see Borůvka's algorithm).

A faster randomized minimum spanning tree algorithm based in part on Borůvka's algorithm due to Karger, Klein, and Tarjan runs in expected time.

Deterministic algorithms that find the minimum spanning tree include Prim's algorithm, Kruskal's algorithm, Reverse-Delete algorithm, and Borůvka's algorithm.

Since there are O(n) edges, this requires O(n log n) time using any of the standard minimum spanning tree algorithms such as Borůvka's algorithm, Prim's algorithm, or Kruskal's algorithm.

These randomized and deterministic algorithms combine steps of Borůvka's algorithm, reducing the number of components that remain to be connected, with steps of a different type that reduce the number of edges between pairs of components.

Additionally, since the Delaunay triangulation is a planar graph, its minimum spanning tree can be found in linear time by a variant of Borůvka's algorithm that removes all but the cheapest edge between each pair of components after each stage of the algorithm.