Time complexity of the analyst's traveling salesman algorithm

Abstract

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 in \cite{Schul-Hilbert,BNV} that solves the Analyst's Traveling Salesman Problem has polynomial time complexity and we determine the sharp exponent.