Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 121-01. An Almost-Linear Approximation Scheme for Edit Distance
Manuscript map · lines 4805–4814
OpenAI@2026-10-07#rem:oai-p-121-01
Authors: OpenAI. Family 121.
Title: An Almost-Linear Approximation Scheme for Edit Distance.
Abstract: We give a uniform randomized approximation scheme for unit-cost edit distance. For every fixed rational ${}varepsilon{}in(0,1)$, it estimates the distance between arbitrary explicitly stored strings of total length N within a factor $1+{}varepsilon$ with probability at least 2/3, in worst-case expected time $N{}{1+o(1)}$ on a logarithmic-word RAM. The algorithm supports polynomially bounded integer alphabets and returns zero deterministically on equal strings.
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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