# HW7 - two nodes such that every vertex is in exactly one...

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Homework #7 Due Date: Wednesday, December 1st, start of class 1. Consider the class of 3-SAT instances in which each of the n variables occur – counting positive and negative appearances combined – in exactly three clauses. Furthermore, no variable will show up twice in the same clause. Show how to find a satisfying assignment using network flow. Hint: How many clauses are there? 2. A cycle cover of a directed graph G is a set of cycles (a cycle must include at least
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Unformatted text preview: two nodes) such that every vertex is in exactly one cycle. Give a polynomial-time algorithm to determine whether G has a cycle cover. Justify your algorithm. 3. Suppose we modify the Ford-Fulkerson algorithm so that it always ﬁnds the path with maximum capacity. Explain how this algorithm could be implemented with running time O ( m 2 log n log C ). Justify your answer. Hint: log 1+1 /x y = O ( x log y )...
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