获得树的最小顶点覆盖率的好的算法是什么? [英] What is a good algorithm for getting the minimum vertex cover of a tree?

问题描述

什么是获取树的最小顶点覆盖率的好算法?

What is a good algorithm for getting the minimum vertex cover of a tree?

节点的邻居.

最小顶点数.

推荐答案

我希望

I hope here you can find more related answer to your question.

我正在考虑我的解决方案，可能您需要完善它，但是只要动态编程位于您的标签之一中，您可能就需要:

I was thinking about my solution, probably you will need to polish it but as long as dynamic programing is in one of your tags you probably need to:

1. 对于每个u顶点，定义S +(u)为顶点u和S-(u)的覆盖大小覆盖没有顶点u.
2. S +(u)= 1 +每个u的子v的和(S-(v)).
3. S-(u)=每个u的孩子v的总和(max {S-(v)，S +(v)}).
4. 答案是max(S +(r)，S-(r))，其中r是树的根.

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阅读此之后.更改了上述算法，以找到最大独立集，因为在Wiki文章中指出

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After reading this. Changed the above algorithm to find maximum independent set, since in wiki article stated

当且仅当补集是顶点覆盖时，集合才是独立的.

A set is independent if and only if its complement is a vertex cover.

因此，通过将min更改为max，我们可以找到最大的独立集，并称赞最小的顶点覆盖，因为这两个问题是等价的.

So by changing min to max we can find the maximum independent set and by compliment the minimum vertex cover, since both problem are equivalent.

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