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final(6) - CS 473U Final Exam Questions Fall 2006 1 A...

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CS 473U Final Exam Questions (December 15, 2006) Fall 2006 1. A double-Hamiltonian circuit in an undirected graph G is a closed walk that visits every vertex in G exactly twice , possibly by traversing some edges more than once. Prove that it is NP-hard to determine whether a given undirected graph contains a double-Hamiltonian circuit. 2. Suppose you are running a web site that is visited by the same set of people every day. Each visitor claims membership in one or more demographic groups ; for example, a visitor might describe himself as male, 31-40 years old, a resident of Illinois, an academic, a blogger, a Joss Whedon fan 1 , and a Sports Racer. 2 Your site is supported by advertisers. Each advertiser has told you which demographic groups should see its ads and how many of its ads you must show each day. Altogether, there are n visitors, k demographic groups, and m advertisers. Describe an efficient algorithm to determine, given all the data described in the previous paragraph, whether you can show each visitor exactly one ad per day, so that every advertiser has its desired number of ads displayed, and every ad is seen by someone in an appropriate demographic group.
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