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CS570_Exam_2__Spring_2007_sol

# CS570_Exam_2__Spring_2007_sol - CS570 Analysis of...

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CS570 Analysis of Algorithms Spring 2007 Exam 2 Name: _____________________ Student ID: _________________ Maximum Received Problem 1 20 Problem 2 10 Problem 3 20 Problem 4 20 Problem 5 20 Problem 6 5 Problem 7 5 Note: The exam is closed book closed notes.

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1) 20 pts Mark the following statements as TRUE or FALSE . No need to provide any justification. [ TRUE/FALSE ] True Max flow problems can in general be solved using greedy techniques. [ TRUE/FALSE ] False If all edges have unique capacities, the network has a unique minimum cut. [ TRUE/FALSE ] True Flow f is maximum flow if and only if there are no augmenting paths. [ TRUE/FALSE ] True Suppose a maximum flow allocation is known. Increase the capacity of an edge by 1 unit. Then, updating a max flow can be easily done by finding an augmenting path in the residual flow graph. [ TRUE/FALSE ] False In order to apply divide & conquer algorithm, we must split the original problem into at least half the size. [ TRUE/FALSE ] True If all edge capacities in a graph are integer multiples of 5 then the maximum flow value is a multiple of 5. [ TRUE/FALSE ] False If all directed edges in a network have distinct capacities, then there is a unique maximum flow . [ TRUE/FALSE ] True Given a bipartite graph and a matching pairs, we can determine if the matching is maximum or not in O(V+E) time [ TRUE/FALSE ] False Maximum flow problem can be efficiently solved by dynamic programming [ TRUE/FALSE ] True The difference between dynamic programming and divide and conquer techniques is that in divide and conquer sub-problems are independent
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CS570_Exam_2__Spring_2007_sol - CS570 Analysis of...

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