winaichan263's blog

Maximum Independent Set on graph with one simple cycle
By winaichan263, history, 8 years ago, In English

Hi. I've just started working on some DP + graph problems recently, but I've gotten stuck on one. It gives you a graph with exactly one simple cycle with no other vertices (all n vertices are on the cycle) and ask you to find the total cost of the maximum independent set of the graph. I know that it is a modification of maximum independent set on trees, but I don't know how to deal with the cycle. The farthest I've gotten is adding the first node as node n+1 and the dp recurrence. Can someone help me?

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8 years ago, # |
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Cut any arbitrary edge u — v in cycle. now the graph is a tree.

There are two cases : 1. MIS without selecting node v 2. MIS without selecting node u

Solving this is a slight modification to maximum independent set on trees.

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    8 years ago, # ^ |
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    Thanks for the comment. I'm already aware of what you said, but I'm not sure how to deal with the doubled cost of the root node.

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      8 years ago, # ^ |
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      eh? I can't understand how cost of root node can be doubled..

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        8 years ago, # ^ |
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        Do you add the first node as the n+1th node? Because if you do, the cost of tye first node is doubled.

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