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- W4319789945 abstract "Pyramidal tours with step-backs are Hamiltonian tours of a special kind: the salesperson starts in city 1, then visits some cities in ascending order, reaches city $n$, and returns to city 1 visiting the remaining cities in descending order. However, in the ascending and descending direction, the order of neighboring cities can be inverted (a step-back). It is known that on pyramidal tours with step-backs the traveling salesperson problem can be solved by dynamic programming in polynomial time. We define the polytope of pyramidal tours with step-backs $operatorname{PSB}(n)$ as the convex hull of the characteristic vectors of all possible pyramidal tours with step-backs in a complete directed graph. The 1-skeleton of $operatorname{PSB}(n)$ is the graph whose vertex set is the vertex set of the polytope, and the edge set is the set of geometric edges or one-dimensional faces of the polytope. We present a linear-time algorithm to verify vertex adjacencies in 1-skeleton of the polytope $operatorname{PSB}(n)$ and estimate the diameter and the clique number of 1-skeleton: the diameter is bounded above by 4 and the clique number grows quadratically in the parameter $n$." @default.
- W4319789945 created "2023-02-11" @default.
- W4319789945 creator A5000594767 @default.
- W4319789945 date "2022-02-07" @default.
- W4319789945 modified "2023-10-02" @default.
- W4319789945 title "On 1-skeleton of the polytope of pyramidal tours with step-backs" @default.
- W4319789945 doi "https://doi.org/10.33048/semi.2022.19.056" @default.
- W4319789945 hasPublicationYear "2022" @default.
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