Transposition is Nearly Optimal for IID List Update
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Statement
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.
Context
List update is one of the founding problems of online algorithms (Sleator-Tarjan 1985), and the standing of Rivest's 1976 transposition rule under stochastic requests is a five-decade question of that community.
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"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."
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