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Optimal Chain Density and Space-Time Tradeoffs for the TSP

Algorithms & optimization · posed by Johnson, Leader and Russell, 2015 · partial

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Statement

The paper nearly settles the tradeoff between the size of a set system over [n][n] and its number of full chains, an extremal question raised by Johnson, Leader and Russell as a counterpart to Sperner-type results, and linked by recent work to the space and time complexity of Bellman–Held–Karp dynamic programming for permutation problems.

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

  1. proof attempt · #1

    Alexandr Andoni, Justin Dallant, László Kozma and Hantao Yu, using ChatGPT 5

    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 assisted
    — a person led the work and used a model along the way.

    The disclosure is one sentence: the results of the paper were obtained with the help of ChatGPT 5. It says the results rather than the exposition, but does not say how much, so the lowest tier applies.

    The authors describe the tradeoff as nearly settled rather than settled.

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

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