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Unformatted text preview: ID number: Page 2 of 11 Problem 1: [10 marks] Use Dantzig’s 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 222 52 12 1 2 The following copies of D are included for your convenience. 2 2 2 b c d e a s f22 52 12 1 2 2 b c d e a s f22 52 12 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 FordFulkerson Algorithm find a maximum value ( s,t )flow and a minimum capacity ( s,t )cut in the digraph above. (The arclabels 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 arccosts ( w uv : uv ∈ A ) and nodedemands ( b v : v ∈ N ). Consider the following linear program ( P )....
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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.
 Fall '05
 various

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