hw2 - 4 Problem#15 BHM Chapter 11 5 Consider the example on...

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ORIE 3310/5310 Optimization II Summer 2009 Homework # 2 Due: Monday, July 13, by 2:30, in the OR3310 homework drop box. These frst Few problems are “practice” problems, not to be handed in. Problems 1 and 4 are From the Bradley, Hax, and Magnanti text, while problems 2,3, and 5 are based on the class lecture notes on shortest paths. 1. Problem #6, BHM Chapter 11. 2. Solve the example on page 2 oF the shortest path notes using Dijkstra’s algorithm. 3. ±or the example on page 6 oF the shortest path notes, change c 42 From 1 to - 6 . Compute the shortest path lengths using Dijkstra’s algorithm. Does the algorithm give the correct solution? Why? (Point out where the validation prooF Fails in the case oF negative edge costs.)
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Unformatted text preview: 4. Problem #15, BHM Chapter 11. 5. Consider the example on page 5 oF the shortest path notes. ±or j = 1 , . . . , 6 , compute the values v j (5) = min 1 ≤ i ≤ 6 { v i (4) + c ij } . Do the values v j (5) di²er From v j (4) ? Why? Now change c 36 From 3 to-3 (the remaining data are unchanged). Re-do the computation For the modifed graph (From scratch!). Are the v j (4) and v j (5) values di²erent? Why? The Following problems are to be handed in. 1. Problem #7, BHM Chapter 11. 2. Problem #17, BHM Chapter 11. 3. Problem #18, BHM Chapter 11. 4. Problem #19, BHM Chapter 11. 5. Problem #22, BHM Chapter 11. 1...
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