3 research outputs found

    On vertex adjacencies in the polytope of pyramidal tours with step-backs

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    We consider the traveling salesperson problem in a directed graph. The pyramidal tours with step-backs are a special class of Hamiltonian cycles for which the traveling salesperson problem is solved by dynamic programming in polynomial time. The polytope of pyramidal tours with step-backs PSB(n)PSB (n) is defined as the convex hull of the characteristic vectors of all possible pyramidal tours with step-backs in a complete directed graph. The skeleton of PSB(n)PSB (n) is the graph whose vertex set is the vertex set of PSB(n)PSB (n) and the edge set is the set of geometric edges or one-dimensional faces of PSB(n)PSB (n). The main result of the paper is a necessary and sufficient condition for vertex adjacencies in the skeleton of the polytope PSB(n)PSB (n) that can be verified in polynomial time.Comment: in Englis

    k-Best constrained bases of a matroid

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