CS570 Exam II Spring 2012 (2)

CS570 Exam II Spring 2012 (2) - CS570 Analysis of...

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CS570 Analysis of Algorithms Spring 2012 Exam II Name: _____________________ Student ID: _________________ ____12:30 PM Section ____2:00 PM Section Maximum Received Problem 1 20 Problem 2 20 Problem 3 20 Problem 4 20 Problem 5 20 Total 100 2 hr exam Close book and notes If a description to an algorithm is required please limit your description to within 200 words, anything beyond 200 words will not be considered. This study resource was shared via CourseHero.com
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1) 20 pts Mark the following statements as TRUE , FALSE . No need to provide any justification. [ FALSE ] If f is a maximum s-t flow in a flow network G, then for all edges e out of s, we have f(e) = c e . [ FALSE ] Let (A, B) be a minimum s-t cut with respect to the capacities { c e : e E}. Now suppose we add 1 to every capacity, then (A,B) is still a minimum s-t cut with respect to these new capacities {1 + c e : e E}. [ TRUE ] If we multiply each edge with t he same positive multiple “f”, the max flow also gets multiplied by the same factor. [ TRUE ] If a problem can be solved by dynamic programming, then it can always be solved by exhaustive search. [ TRUE ] Sequence alignment problem between sequence X and sequence Y can be solved using dynamic programming in O(mn) when |X| = m and |Y| = n. [ FALSE ] Bellman-Ford algorithm cannot solve the shortest path problem in graphs with negative cost edges in polynomial time. [ FALSE ] If a dynamic programming solution is set up correctly, i.e. the recurrence equation is correct and the subproblems are always smaller than the original problem, then the resulting algorithm will always find the optimal solution in polynomial time. [ TRUE ] In the Ford Fulkerson algorithm, choice of augmenting paths can affect the number of iterations. [ FALSE ] If in a flow network all edge capacities are distinct, then there exists a unique min-cut. [ TRUE ] Max flow in a flow network can be found in polynomial time.
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  • Fall '11
  • Arthur
  • Trigraph, ar stu, Shortest path problem, Flow network, Maximum flow problem, Max-flow min-cut theorem

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