CS70_Exam__Fall_2007

# CS70_Exam__Fall_2007 - CS570 Analysis of Algorithms Fall...

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CS570 Analysis of Algorithms Fall 2007 Exam Name: _____________________ Student ID: _________________ DEN (circle YES/NO) Maximum Received Problem 1 20 Problem 2 15 Problem 3 20 Problem 4 10 Problem 5 20 Problem 6 15 Total 100 Note: The exam is closed book closed notes.

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1) 20 pts Mark the following statements as TRUE , FALSE . No need to provide any justification. [ TRUE/FALSE ] The runtime of Ford-Fulkerson is bounded by O( E*f ), where E is the number of edges in the graph and f is the maximum flow in the graph and capacities are real. [ TRUE/FALSE ] If all edge capacities in a graph are integer multiples of 5 then the maximum flow value is a multiple of 5. [ TRUE/FALSE ] For any graph with edge capacities and vertices s and t, there always exists an edge such that increasing the capacity on that edge will increase the maximum flow from s to t in G. (Assume that there is at least one path in the graph from s to t.) [ TRUE/FALSE ] Let G be a flow diagram (a directed graph with edge capacities) and let k be a positive number. Then there is a flow through G of size k if and only if the edges out
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