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### HW7

Course: CSCI CSCI570, Spring 2010
School: USC
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Word Count: 148

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#7 Due Homework 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 nd a satisfying assignment using network ow. Hint: How many clauses are there? 2. A cycle cover of a directed graph G...

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#7 Due Homework 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 nd a satisfying assignment using network ow. Hint: How many clauses are there? 2. A cycle cover of a directed graph G is a set of cycles cycle (a must include at least 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 nds the path with maximum capacity. Explain how this algorithm could be implemented with running time O(m2 log n log C ). Justify your answer. Hint: log1+1/x y = O(x log y )
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
Math 235 - Final Exam Fall 2009NOTE: The questions on this exam does not exactly reect which questions will be on this terms exam. That is, some questions asked on this exam may not be asked on our exam and there may be some questions on our exam not ask
Waterloo - MATH - 235/237
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Waterloo - MATH - 235/237
Math 235 - Final Exam Spring 2009NOTE: The questions on this exam does not exactly reect which questions will be on this terms exam. That is, some questions asked on this exam may not be asked on our exam and there may be some questions on our exam not a