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(A Refinement of the Termination Tolerance) Show that the assignment obtained upon termination of the auction algorithm is within (n-1) of being optimal (rather than n). Also, for every n ≥ 2, construct an example of an assignment problem with integer data such that the auction algorithm terminates with a nonoptimal assignment when = 1/(n - 1). (Try first n = 2 and n = 3, and generalize.)

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