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- W330417094 abstract "$ newcommand{R}{{mathbb R}} newcommand{atspp}{text{ATSPP}} newcommand{atsp}{text{ATSP}} newcommand{lt}{ell} $ We consider a variant of the traveling salesman problem (TSP): Given a directed graph $G=(V,A)$ with non-negative arc lengths $lt,:, A rightarrow R^+$ and a pair of vertices $s,t$, find an $s$-$t$ walk of minimum length that visits all the vertices in $V$. If $lt$ satisfies the asymmetric triangle inequality, the problem is equivalent to that of finding an $s$-$t$ path of minimum length that visits all the vertices. We refer to this problem as the asymmetric traveling salesman path problem $(atspp)$. When $s = t$ this is the well known asymmetric traveling salesman tour problem $(atsp)$. Although an $O(log n)$ approximation ratio has long been known for $atsp$, the best known ratio for $atspp$ is $O(sqrt{n})$. In this paper we present a polynomial time algorithm for $atspp$ that has an approximation ratio of $O(log n)$. The algorithm generalizes to the problem of finding a minimum length path or cycle that is required to visit a subset of vertices in a given order." @default.
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- W330417094 date "2007-01-01" @default.
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- W330417094 doi "https://doi.org/10.4086/toc.2007.v003a010" @default.
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