Unformatted text preview: vertices in set S after each iteration of the while loop. 6 3 2 1 4 2 7 5 3 6 4. (1 Points) p.600: 24.34 We are given a directed graph ) , ( E V G = on which each edge E v u ∈ ) , ( has an associated value ) , ( v u r , which is a real number in the range 1 ) , ( ≤ ≤ v u r that represents the reliability of a communication channel from vertex u to vertex v . We interpret ) , ( v u r as the probability that the channel from u to v will not fail, and we assume that these probabilities are independent. Give an efficient algorithm to find the most reliable path between two given vertices. 5. (1 Point) p.613: 24.54 Let ) , ( E V G = be a weighted, directed graph with source vertex s and let G be initialized by INITIALIZESINGLESOURCE( G , s ). Prove that if a sequence of relaxation steps sets ] [ s to a nonNIL value, then G contains a negativeweight cycle. s y t z x...
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 Spring '09
 AgoreBack
 Topology, Graph Theory, Shortest path problem, shortest path, source vertex

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