Abstract
We solve the recognition problem for permuted Demidenko matrices. This problem is relevant in the context of hard combinatorial optimization problems becoming tractable if the input is a Demidenko matrix. For example the TSP is polynomially solvable for Demidenko distance matrices. In the TSP context we look for a renumbering of the cities resulting in a Demidenko distance matrix, thus in a polynomially solvable case. We can find such a renumbering of n cities in O(n4) time, if it exists.
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