CO-351-1079-Midterm_exam

# CO-351-1079-Midterm_exam - CO 351 Midterm Examination 1 CO...

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CO 351 - Midterm Examination 1 CO 351 Network Flow Theory Midterm Examination October 22, 2007 7:00 – 8:30 p.m. Instructor: Ashwin Nayak Instructions Please print your name and student identifcation 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 will be allowed on the midterm. When solving a numerical example, show all of your work. (You do not have to show how you added, divided, etc., just what you added, divided, etc., and the result.) I± you require more space to present your solution, please use the back o± the previous page. Indicate clearly where your solution continues.

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2 Question 1. Let D = ( N,A ) be a digraph with s,t N , s n = t , with arc-lengths w R A . Part 1.1 [4 marks] Prove that there is an st -dipath in D if and only if for every ( s,t )-separator S N , we have δ out ( S ) n = . Part 1.2 [3 marks] Suppose there is an sv -dipath for every v N . DeFne y v as the length of a shortest sv - dipath in D . Prove that if D has no negative dicycle, then y v is a feasible potential. Part 1.3
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## This note was uploaded on 11/18/2010 for the course CO 351 taught by Professor Various during the Fall '05 term at Waterloo.

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CO-351-1079-Midterm_exam - CO 351 Midterm Examination 1 CO...

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