Successive minimum spanning trees
RANDOM STRUCTURES & ALGORITHMS（2022）
摘要
In a complete graph Kn with independent uniform(0,1) (or exponential(1)) edge weights, let T1 be the minimum-weight spanning tree (MST), and Tk the MST after deleting the edges of all previous trees. We show that each tree's weight w(Tk) converges in probability to a constant gamma k, with 2k-2k更多
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关键词
discrete probability,functional fixed point,inhomogeneous random graph,Kruskal's algorithm,minimum spanning tree,multi-type branching process,optimization in random structures,robust optimization,second-cheapest structure
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