A physical study of the LLL algorithm

Jintai Ding,Seungki Kim,Tsuyoshi Takagi,Yuntao Wang,Bo-Yin Yang

Journal of Number Theory（2023）

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摘要

This paper presents a study of the LLL algorithm from the perspective of statistical physics. Based on our experimental and theoretical results, we suggest that interpreting LLL as a sandpile model may help understand much of its mysterious behavior. In the language of physics, our work presents evidence that LLL and certain 1-d sandpile models with simpler toppling rules belong to the same universality class.

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关键词

Lattice reduction,LLL algorithm,Sandpile models,Finite-size scaling theory

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