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Expected linear time MST algorithm : ウィキペディア英語版 | Expected linear time MST algorithm A randomized algorithm for computing the minimum spanning forest of a weighted graph with no isolated vertices. It was developed by David Karger, Philip Klein, and Robert Tarjan. The algorithm relies on techniques from Borůvka's algorithm along with an algorithm for verifying a minimum spanning tree in linear time.〔 〕 It combines the design paradigms of divide and conquer algorithms, greedy algorithms, and randomized algorithms to achieve expected linear performance. Deterministic algorithms that find the minimum spanning tree include Prim's algorithm, Kruskal's algorithm, reverse-delete algorithm, and Borůvka's algorithm. ==Overview== The key insight to the algorithm is a random sampling step which partitions a graph into two subgraphs by randomly selecting edges to include in each subgraph. The algorithm recursively finds the minimum spanning forest of the first subproblem and uses the solution in conjunction with a linear time verification algorithm to discard edges in the graph that cannot be in the minimum spanning tree. A procedure taken from Borůvka's algorithm is also used to reduce the size of the graph at each recursion.
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