Maximum Independent Set in Trees (Linear Time Algorithm)

Here we give a linear time algorithm for the maximum independent set problem for trees. A tree is a graph without cycles, and an independent set is a set of vertices without edges between them. The trick here is that trees don't have cycles, so answering a question about a vertex and its neighbors partitions the rest of the vertices into "clusters" that have no vertices in common. So we can solve the problem independently for each of the neighbors.

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