OpenAI · 121-01 · 2026-09-24 · Theoretical computer science
An Almost-Linear Approximation Scheme for Edit Distance
preprints/An-Almost-Linear-Approximation-Scheme-for-Edit-Distance-September-24-2026
Family 121. Almost-linear expected-time approximation of edit distance.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
For every fixed rational , gives a randomized approximation to unit-cost edit distance in worst-case expected time , with success probability at least . The strings have total length and polynomially bounded integer symbols. This is an asymptotic guarantee at fixed accuracy.
We give a uniform randomized approximation scheme for unit-cost edit distance. For every fixed rational , it estimates the distance between arbitrary explicitly stored strings of total length N within a factor with probability at least 2/3, in worst-case expected time on a logarithmic-word RAM. The algorithm supports polynomially bounded integer alphabets and returns zero deterministically on equal strings.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 121: Almost-linear approximation of edit distance. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.