MST的cheriton-tarjan算法的复杂度答案

【问题标题】：complexity of cheriton-tarjan algorithm for MSTMST的cheriton-tarjan算法的复杂度
【发布时间】：2014-02-15 15:47:11
【问题描述】：

几天前，我在这里看到一篇关于 Cheriton-Tarjan 算法的帖子，我认为这是对 Boruvka 算法的改进。我想我知道它是如何工作的，但我不明白为什么这个算法的复杂度是 O(mloglogn)。有人可以向我解释一下吗？谢谢。

【问题讨论】：

标签： time-complexity minimum-spanning-tree

【解决方案1】：

没错，这个算法的复杂度是 O(mlog(logn))。阅读这篇文章here，我想你会理解算法及其复杂性

【讨论】：

【解决方案2】：

Here is a reference to the 1976 paper and the complexity you quote
is only for some worse case situations. There are other complexities
quoted for other conditions.

Finding Minimum Spanning Trees

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Article Data
History
Submitted: 10  June  1975
Published online: 13 July 2006
Keywords
equivalence algorithm, graph algorithm, minimum spanning tree, priority queue
Digital Object Identifier
http://dx.doi.org/10.1137/0205051
Publication Data
ISSN (print): 0097-5397
ISSN (online): 1095-7111
Publisher: Society for Industrial and Applied Mathematics
David Cheriton and Robert Endre Tarjan

This paper studies methods for finding minimum spanning trees in graphs.
Results include 1.  several algorithms with $O(m\log \log n)$ worst-case
running times, where n is the number vertices and m is the number of
edges in the problem graph; 2.  an $O(m)$ worst-case algorithm for dense
graphs (those for which m is $\Omega (n^{1 + \varepsilon } )$ for some
positive constant $\varepsilon $); 3.  an $O(n)$ worst-case algorithm
for planar graphs; 4.  relationships with other problems which might
lead general lower bound for the complexity of the minimum spanning tree
problem.

Copyright © 1976 Society for Industrial and Applied Mathematics

Read More: http://epubs.siam.org/doi/abs/10.1137/0205051

【讨论】：