The number written next to each link of the network shown below is the probability of the link failing during the lifetime of a virtual circuit from node A to node B. It is assumed that links fail independently of each other. Find the most reliable path from A to B. This problem is equivalent to finding the path with minimum cost, for which we can use Dijkstra's algorithm, as shown in the table below the graph. Show your work. A 0.03 Step 0 1 2 3 4 5 6 ● ● 0.07 C 0.01 E N' {A} {A.C} {A,C,..} {A,C......} {A.C.........} {A.C............} .... **** D(B), p(B) 00.- **** *** 0.05 **** 0.02 0.04 ******* .... ... D **** *** 0.01 ... 0.02 F D(C), p(C) D(D), p(D) | D(E), p(E) | D(F), p(F) ..., A 0.07, A 00,- 00,- 0.08, C ... 0.06 **** 0.03 G **** *** 0.03 B D(G), p(G) ∞, - .... ... ... {A,C, ..........} You do not need to fill an entry at a given step if it is not changing during this step If several entries should be changed at a given step, follow the order of the columns starting at left and going right.

The number written next to each link of the network shown below is the probability of the link failing during the lifetime of a virtual circuit from node A to node B. It is assumed that links fail independently of each other. Find the most reliable path from A to B. This problem is equivalent to finding the path with minimum cost, for which we can use Dijkstra's algorithm, as shown in the table below the graph. Show your work. A 0.03 Step 0 1 2 3 4 5 6 ● ● 0.07 C 0.01 E N' {A} {A.C} {A,C,..} {A,C......} {A.C.........} {A.C............} .... ** D(B), p(B) 00.- * 0.05 0.02 0.04 * .... ... D * 0.01 ... 0.02 F D(C), p(C) D(D), p(D) | D(E), p(E) | D(F), p(F) ..., A 0.07, A 00,- 00,- 0.08, C ... 0.06 ** 0.03 G * 0.03 B D(G), p(G) ∞, - .... ... ... {A,C, ..........} You do not need to fill an entry at a given step if it is not changing during this step If several entries should be changed at a given step, follow the order of the columns starting at left and going right.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter9: Integer Programming

Section9.6: Solving Combinatorial Optimization Problems By The Branch-and-bound Method

Problem 3P

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