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Pré-Publication, Document De Travail Année : 2023

Assouad-Nagata dimension and gap for ordered metric spaces

Résumé

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.

Dates et versions

hal-03958883 , version 1 (26-01-2023)

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Anna Erschler, Ivan Mitrofanov. Assouad-Nagata dimension and gap for ordered metric spaces. 2023. ⟨hal-03958883⟩
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