Year: 2025
Type: article
Abstract: The performance of witness-based random search algorithms is highly influenced by the distribution density of witnesses. To optimize this distribution, we propose a novel method based on the symmetric folding of the objective dataset. Our approach involves establishing mathematical models for symmetrically folding points and regions in two-dimensional space and deriving a set of rigorously proven properties for folding operations on matrix-formed datasets, complete with computational formulations. Theoretical analysis and numerical experiments demonstrate that the proposed symmetric folding technique can nearly double the probability of successfully identifying a target element via random sampling. The efficacy of the method is validated by a case study on identifying a nontrivial divisor of an odd composite integer, demonstrating that the symmetric folding of the structured dataset can significantly improve the efficiency of randomized search procedures.
Source: Symmetry
DOI: 10.3390/sym17122086
Author: Xingbo Wang
Institution: Foshan University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Award: G6308190857
OpenAlex ID: W4417036883