assignment 6 Sol - CS 331 Algorithms and Complexity(Spring...

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CS 331: Algorithms and Complexity (Spring 2016) Unique numbers: 51035, 51040, 51055, 51060 Assignment 6 Due on Wednesday, March 30, by 11.59pm Honor Code As a student of The University of Texas at Austin, I shall abide by the core values of the University and uphold academic integrity . Student Judicial Services O ce of the Dean of Students Division of Student A airs We are giving you these solutions as review material to help you study for the rest of the course. Please do not share them with future students of CS 331 or post them on external sites.
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Assignment 6 Problem 1 Problem 1 (10 points) Let G = ( V, E ) be a flow network, with a source s , a sink t , and a positive integer capacity c e on every edge e . State whether each of the following is True or False. If True, you have to justify your answer. If False, you have to provide a counter example and show your work. 1. Let Q V , such that Q does not contain either of s or t . Then, f out ( Q ) - f in ( Q ) = 0. Sol. This is true. Conservation condition. For the nodes in Q, what flows in, flows out. 2. If f is a maximum s-t flow in G , then f saturates every edge out of s with flow (i.e., for all edges e out of s , we have f ( e ) = c e ).
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