Abstract
In this paper, we develop two algorithms for finding a directed path of minimum rank-two monotonic cost between two specified nodes in a network with n nodes and m arcs. Under the condition that one of the vectors characterizing the cost function f is binary, one yields an optimal solution in O(n3) or O(nm log n) time if f is quasiconcave; the other solves any problem in O(nm + n 2 log n) time.
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Kuno, T. Polynomial algorithms for a class of minimum rank-two cost path problems. Journal of Global Optimization 15, 405–417 (1999). https://doi.org/10.1023/A:1008372614175
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DOI: https://doi.org/10.1023/A:1008372614175