Show that there exists at least one node j

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Reference no: EM131122513

Consider the one origin-all destinations problem and the generic algorithm of Section 2.2. Assume that there exists a path that starts at node 1 and contains a cycle with negative length. Assume also that the generic algorithm is operated so that if a given node belongs to the candidate list for an infinite number of iterations, then it also exits the list an infinite number of times. Show that there exists at least one node j such that the sequence of labels dj generated by the algorithm diverge to -∞. Hint: Argue that if the limits dj of all the label nodes are finite, then we have dj ≤ di + aij for all arcs (i, j).

Reference no: EM131122513

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