(10pts) We are given a communication network that is an edge-weighted graph G=(V, E). The weight on each edge is at least 0 and at most 1, representing the reliability of the communication channel: it is the probability that the communication between the two endpoints will not fail. Design an O(|E| log??|E|)? time algorithm to find the most reliable path between two given nodes. Describe its pseudo code, correctness proof and running time proof.

(Note: Understand correctly what the question states. On the graph in the figure: - The path {S, X, T} does not fail with the probability 0.90.4=0.36=36% - The path {S, X, Y, T} does not fail with the probability 0.90.99.8=0.64=64% - Try {S, Y, T} and {S, Y, X, T} to conclude {S, X, Y, T} is the most reliable path.)