A set of n cities is to be connected via communication links. The cost to construct a link between cities i and j is Cij , i = j . Enough links should be constructed so that for each pair of cities there is a path of links that connects them. As a result, only n − 1 links need be constructed. A minimal cost algorithm for solving this problem (known as the minimal spanning tree problem)

first constructs the cheapest of all the

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links. Then, at each additional stage it chooses the cheapest link that connects a city without any links to one with links. That is, if the first link is between cities 1 and 2, then the second link will either be between 1 and one of the links 3, . . . , n or between 2 and one of the links 3, . . . , n. Suppose that all of the

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costs Cij are independent exponential random variables with mean 1. Find the expected cost of the preceding algorithm if

(a) n = 3,

(b) n = 4.