Question
[Dijkstras algorithm application] Consider the problem defined below. [Most reliable path finding problem] Consider a connected weighted graph (V, E). where each edge weight r(u,v)
[Dijkstras algorithm application] Consider the problem defined below. [Most reliable path finding problem] Consider a connected weighted graph (V, E). where each edge weight r(u,v) of an edge (u, v) E is in the range of 0to 1, i.e.,0 r(u,v) 1. This edge weight is the reliability of a direct communication channel from u to vthat is, the probability that the channel from u to v will not fail. The reliability of a path from anode to another node is then defined as the product of the weights of all edges constituting the path. Our goal is to find a most reliable path between two input nodes, that is, a path of which the reliability is the highest among all possible paths between the two input nodes. We can use the Dijkstras shortest path finding algorithm to solve this problem, that is, find the most reliable path from a node s to another node t. Discuss how. Your answer should describe the specific steps of converting this most-reliable-path-finding problem to a shortest-path-finding problem. There is no need to write the pseudocode of an algorithm. Note Dijkstras algorithm requires that all edge weights must be non-negative. You may find the following point helpful: log(i pi)= i log pi.
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