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Quadratic-Time Hardness of Furthest Pair in Superconstant Dimension

Theoretical computer science · posed by fine-grained complexity literature · solved

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Statement

Furthest Pair and its relatives admit f(d) n2−Θ(1/d)f(d)\,n^{2-\Theta(1/d)} algorithms, making them the standard examples of barely subquadratic computation, and whether that is optimal in superconstant dimension was open. Under SETH it is: Furthest Pair requires quadratic time once the dimension is superconstant.

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

  1. proof attempt · #1

    Barna Saha, Yinzhan Xu and Christopher Ye, using ChatGPT 5.5 Pro (with Codex, Claude Opus, Gemini for feedback)

    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.

    The paper states the proof was initially discovered by ChatGPT 5.5 Pro, that the initial prompt was essential, and that other systems were used to generate feedback on it. The authors validated and substantially edited the proof to improve it.

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

open in Claude →open in ChatGPT →

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