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The Thin Matching Problem

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anari-charikar-thin-matchingAlgorithms & optimizationposed by Nima Anari, Moses Charikar, Prasanna Ramakrishnan, 2023recorded: partial

1 attempt · no person has looked

Statement

Anari, Charikar and Ramakrishnan asked whether every fractional perfect matching admits a perfect matching that is α\alpha-thin with respect to it, meaning it crosses every cut at most α\alpha times the fractional amount. Resolved up to polylogarithmic factors.

Context

up to polylogarithmic factors

A problem posed at STOC-level in 2023, connected to thin-tree questions and the asymmetric travelling salesman literature.

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1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.5 Pro with Alireza Haqi, Shayan Oveis Gharan ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    GPT-5.5 Pro
    people
    Alireza Haqi, Shayan Oveis Gharan

    The acknowledgement says the authors used GPT-5.5 Pro during the research, and points at the connection to cut-tree sparsification as where it mattered.

    up to polylogarithmic factors

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