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A New Gap Sequence for Shellsort: RL-Driven Algorithm Discovery Beyond $N^{4/3}$

arXiv · AI, language, vision and robotics · article · Sep 24, 2026 · UTC

Choosing Shellsort gaps is a well-known open problem. For over sixty years, successful sequences have relied on human-designed formulas, numerical searches, or number-theoretic constructions. Although stronger general bounds exist for dense or mainly theoretical families, the worst-case upper bound for a short, sparse, and practically competitive construction has not advanced beyond $N^{4/3}$ for decades. We ask whether the sequence itself can instead be learned from execution. We present an RL-driven, self-supervised system that searches over executable gap generators. Every proposal is valid

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