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The Arborescence-Sampling Barrier for Eulerian Tours

Algorithms & optimization · posed by arborescence-sampling literature · solved

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Statement

Sampling a nearly uniform Eulerian tour of a directed Eulerian multigraph was stuck at mnmn-type running times coming from arborescence sampling. A randomized algorithm achieves O~(m3/2)\widetilde{O}(m^{3/2}) worst case, breaking that barrier on sparse graphs.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Nima Anari, using GPT-5.5 Pro Extended, Codex

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    A clean division of labour, stated as such: the author conjectured the mixing theorem underlying the analysis, and GPT-5.5 Pro Extended produced its linear-algebra proof. Codex assisted with manuscript assembly.

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