Abstract
In this paper an inverse problem of the weighted shortest path problem is discussed in which a path is given and we need to find weighted length vectors under which the path becomes the shortest one. It is found that all such length vectors form a polyhedral cone. Algebraic and graphic characters of the extreme directions of the solution cone are then exposed that show the relation between this problem and the minimal cutset problem in graph theory.
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The author gratefully acknowledges the partial support of AFOSR (Grant 90-0008).
The author gratefully acknowledges the partial support of the Croucher Foundation.
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Xu, S., Zhang, J. An inverse problem of the weighted shortest path problem. Japan J. Indust. Appl. Math. 12, 47–59 (1995). https://doi.org/10.1007/BF03167381
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DOI: https://doi.org/10.1007/BF03167381