VibeMathedMath problems solved by AI

Transposition is Nearly Optimal for IID List Update

In the list update problem, is the simple transposition rule optimal under IID requests? The question traces to Rivest's 1976 study of self-organizing lists. The paper proves transposition is within a small constant factor of the optimal online algorithm under any IID distribution.

Result
Proved
Status
Resolved
AI contribution
AI-assisted
Method
Argument
Field
Online algorithms
Posed by
Ronald Rivest (transposition heuristic)
Year posed
1976
Years open
50y
Solved
2026-03-10
Model
GPT-5 Pro
Vendor
OpenAI
Collaborators
Christian Coester
Verification
Unreviewed
Publication
Preprint
Significance
15 / 100
Disclosed cost
Wikipedia
No dedicated article

What the AI did

"The AI generated the idea that the inequality might hold, and hypothesized, based on experiments with small n, that coefficients of the corresponding polynomial appear to be nonnegative. Although the AI was unable to prove these statements... these suggestions were essential for motivating the proof approach pursued in this paper."

Source

arXiv

Discussion