There is a network of roads G = (V, E) connecting a set of cities V. Each road in E has an associated length le. There is a proposal to add one new road to this network, and there is a list E′ of pairs of cities between which the new road can be built. Each such potential road e′ ∈ E′ has an associated length. As a designer for the public works department you are asked to determine the road e′ ϵ E′ whose addition to the existing network G would result in the maximum decrease in the driving distance between two fixed cities s and t in the network. Give an efficient algorithm for solving this problem.
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