Time complexity of the Analyst's Traveling Salesman algorithm

02/21/2022

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by   Anthony Ramirez, et al.

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The Analyst's Traveling Salesman Problem asks for conditions under which a (finite or infinite) subset of ℝ^N is contained on a curve of finite length. We show that for finite sets, the algorithm constructed by Schul (2007)and Badger-Naples-Vellis (2019) that solves the Analyst's Traveling Salesman Problem has polynomial time complexity and we determine the sharp exponent.