CO-351-1075-Final_exam

CO-351-1075-Final_exam - ID number: Page 2 of 11 Problem 1:...

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Unformatted text preview: ID number: Page 2 of 11 Problem 1: [10 marks] Use Dantzigs Algorithm to either find a tree of shortest dipaths rooted at s or find a negative dicycle in the digraph below. (Start with the tree indicated in bold. Briefly describe each step.) 2 b c d e a s f 2-2-2 5-2 1-2 1 2 The following copies of D are included for your convenience. 2 2 2 b c d e a s f-2-2 5-2 1-2 1 2 2 b c d e a s f-2-2 5-2 1-2 1 2 ID number: Page 3 of 11 (0, 3) (1, 3) (5, 6) (3, 3) (1, 4) (2, 2) (4, 5) t (2, 2) (3, 3) (2, 5) c d e a s b Problem 2: [10 marks] Using the Ford-Fulkerson Algorithm find a maximum value ( s,t )-flow and a minimum capacity ( s,t )-cut in the digraph above. (The arc-labels indi- cate ( x uv , c uv ); start with the feasible ( s,t )-flow ( x uv : uv A ). Show your working.) ID number: Page 4 of 11 Problem 3: [10 marks] Let D = ( N,A ) be a digraph with arc-costs ( w uv : uv A ) and node-demands ( b v : v N ). Consider the following linear program ( P )....
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CO-351-1075-Final_exam - ID number: Page 2 of 11 Problem 1:...

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