Time complexity of the Analyst's Traveling Salesman algorithm

TL;DR

This paper analyzes the time complexity of the Analyst's Traveling Salesman algorithm, demonstrating it is polynomial for finite sets and identifying the precise exponent, thus advancing understanding of its computational efficiency.

Contribution

The paper establishes that the Analyst's Traveling Salesman algorithm has polynomial time complexity for finite sets and determines the exact exponent, providing clarity on its computational performance.

Findings

The algorithm is polynomial time for finite sets.

The sharp exponent of the polynomial time complexity is identified.

The results clarify the algorithm's efficiency in practical applications.

Abstract

The Analyst's Traveling Salesman Problem asks for conditions under which a (finite or infinite) subset of $\mathbb{R}^N$ 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.