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- W2254574817 abstract "In the traveling salesman problem (TSP), we are given a complete graph $K_n$ together with an integer weighting $w$ on the edges of $K_n$, and we are asked to find a Hamilton cycle of $K_n$ of minimum weight. Let $h(w)$ denote the average weight of a Hamilton cycle of $K_n$ for the weighting $w$. Vizing in 1973 asked whether there is a polynomial-time algorithm which always finds a Hamilton cycle of weight at most $h(w)$. He answered this question in the affirmative and subsequently Rublineckii, also in 1973, and others described several other TSP heuristics satisfying this property. In this paper, we prove a considerable generalization of Vizing's result: for each fixed $k$, we give an algorithm that decides whether, for any input edge weighting $w$ of $K_n$, there is a Hamilton cycle of $K_n$ of weight at most $h(w)-k$ (and constructs such a cycle if it exists). For $k$ fixed, the running time of the algorithm is polynomial in $n$, where the degree of the polynomial does not depend on $k$ (i.e., the generalized Vizing problem is fixed-parameter tractable with respect to the parameter $k$)." @default.
- W2254574817 created "2016-06-24" @default.
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- W2254574817 date "2016-01-01" @default.
- W2254574817 modified "2023-10-18" @default.
- W2254574817 title "Parameterized Traveling Salesman Problem: Beating the Average" @default.
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- W2254574817 doi "https://doi.org/10.1137/140980946" @default.
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