practice midterm 1

# practice midterm 1 - the total number of streets that you...

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CME305 Sample Midterm I 1. Matchings and Independent Sets Assume that you are given graph G ( V,E ), a matching M in G and inde- pendent S in G . Show that | M | + | S | ≤ | V | . 2. Unique Minimum s-t Cut Given a network G ( V,E,s,t ), give a polynomial time algorithm to deter- mine whether G has a unique minimum s-t cut. 3. Chinese Postman Problem Imagine that you are a postman. You park your truck in your district, and you want to walk around delivering mail to every street in the district and then return to your truck. Also, you are eﬃcient so you want to minimize
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Unformatted text preview: the total number of streets that you have to visit. This can be formulated as a graph problem: given a connected graph G ( V,E ), ﬁnd a closed walk of minimum length that traverses every edge at least once. (a) Give a polynomial time algorithm that gives a closed walk of length at most 2 | E | . (b) (Harder) Give a polynomial time algorithm that gives a closed walk of length at most | E | + | V | -1. 1...
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