2021/09/24 by Anna Erschler, Ivan Mitrofanov, Erschler, Anna +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Topology and Set Theory #Economic theories and models #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2109.12181
openalex publication_date 2021/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We prove that all spaces of finite Assouad-Nagata dimension admit a good order for Travelling Salesman Problem, and provide sufficient conditions under which the converse is true. We formulate a conjectural characterisation of spaces of finite AN-dimension, which would yield a gap statement for the efficiency of orders on metric spaces. Under assumption of doubling, we prove a stronger gap phenomenon about all orders on a given metric space.