One modification to this algorithm improves on its running time by replacing its primary data structure with a number of leftist binary trees, which can be easily merged; that modification is the Cheriton-Tarjan algorithm.
One modification to this algorithm improves on its running time by replacing its primary data structure with a number of leftist binary trees, which can be easily merged; that modification is the Cheriton-Tarjan algorithm. The amortized run-time of one subsection of this algorithm is a notable instance of the inverse Ackermann function appearing in time complexity. The optimizations of "union by rank" and "path compression" can be used to improve on a subsection of this algorithm known as the union-find algorithm. This algorithm has running time "Big O of (*) E log E" where E is the number of edges, since the dominating step in this algorithm is sorting the edges by weight. It works by iteratively choosing the lowest weight edge that connects two previously unconnected components in the graph. For 10 points, name this graph algorithm that, like Boruvka's algorithm and Prim's algorithm, finds the minimum spanning tree of a graph.
One modification to this algorithm improves on its running time by replacing its primary data structure with a number of leftist binary trees, which can be easily merged; that modification is the Cheriton-Tarjan algorithm.
Kruskal's Algorithm