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Optimal Chain Density and Space-Time Tradeoffs for the TSP

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tsp-optimal-chain-densityAlgorithms & optimizationposed by Johnson, Leader and Russell, 2015recorded: partial

1 attempt · no person has looked

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.

Context

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

A 2015 extremal question with a direct bearing on the complexity of classical dynamic programming for permutation problems.

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  • #1

    Attempt 1

    proof attemptChatGPT 5 with Alexandr Andoni, Justin Dallant, László Kozma, Hantao Yu ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT 5
    people
    Alexandr Andoni, Justin Dallant, László Kozma, Hantao Yu

    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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