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3. Consider the following algorithm for the vertex cover problem for trees. Pick an edge (u, v), where u is a leaf. Include v in

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3. Consider the following algorithm for the vertex cover problem for trees. Pick an edge (u, v), where u is a leaf. Include v in the cover, delete all edges incident to v, and repeat until there are no edges left. Show that this algorithm finds a smallest cover. Hint: you may argue using matchings as in the analysis of the 2-approximation algorithm

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