CO-351-1079-Final_exam

CO-351-1079-Final_exam - CO 351 - Final Examination 1 CO...

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Unformatted text preview: CO 351 - Final Examination 1 CO 351 Network Flow Theory Final Examination December 6, 2007 12:30 3:00 p.m. Instructor: Ashwin Nayak Instructions Please print your name and student identification number. NAME STUDENT IDENTIFICATION NUMBER Make sure you have all eleven pages (including this cover page). Only the Faculty approved calculators with the Pink Tie stickers are allowed on the exam. If you require more space to present your solution, please use the back of the previous page. Indicate clearly where your solution continues. Read the questions carefully and ensure that you provide all the details requested. CO 351 - Final Examination 2 Question 1. [10 marks] Find an arborescence of shortest dipaths rooted at node 1 in the following digraph with arc-weights by running the Dual Algorithm. Start with the node labels on the top left copy of the digraph as the initial potential. Using as many copies of the digraph as you need, show the feasible potential by labeling the nodes, draw the equality arcs in bold, show the separator you pick, and indicate the increase in potential in each iteration of the algorithm. 1 2 3 4 5 6 7-4 1 2 1 2 3 3 5-6 5-1-2 6 3 1-4 7 6 5 4 3 Iteration 3 Iteration 4 Iteration 5 4-8-4-7 3 1 2 3 4 5-4-1 5-2 1 3 3 2 2 6-6 5 7 6 Iteration 2 6-2-1 5-6 5 3 2 Iteration 1 Initial potentials-2-1 5-6 5 3 2 1 2 6 3 1-4 7 6 5 4 3 2 1...
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CO-351-1079-Final_exam - CO 351 - Final Examination 1 CO...

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