Question

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性是O（mloglogn）。有人可以向我解释一下吗？日Thnx。

Answer 1

确实，该算法的复杂性为O（mlog（logn））。阅读这篇文章here，我想你会理解算法及其复杂性

Answer 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

MST的Cheriton-tarjan算法的复杂性

2 个答案: