Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 117-02. Near-square-root logarithmic integrality gaps for uniform sparsest cut
Manuscript map · lines 4755–4764
OpenAI@2026-10-07#rem:oai-p-117-02
Authors: OpenAI. Family 117.
Title: Near-square-root logarithmic integrality gaps for uniform sparsest cut.
Abstract: We construct uniform sparsest-cut instances whose Goemans–Linial semidefinite integrality gap is at least $c{}sqrt{{}log n}/({}log{}log n){}3$ along a sequence $n{}to{}infty$. The demand is one between every pair of distinct vertices, and the capacities are nonnegative real numbers. This matches the Arora–Rao–Vazirani upper bound up to a power of ${}log{}log n$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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