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We consider the linearization problem associated with the quadratic travelingsalesman problem (QTSP). Necessary and sufficient conditions are given for acost matrix $Q$ of QTSP to be linearizable. It is shown that these conditionscan be verified in $O(n^5)$ time. Some simpler sufficient conditions forlinearization are also given along with related open problems.

A characterization of Linearizable instances of the Quadratic Traveling Salesman Problem