{"ID":2835975,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.00111","arxiv_id":"2512.00111","title":"An O(1) Space Algorithm for N-Dimensional Tensor Rotation: A Generalization of the Reversal Method","abstract":"The rotation of multi-dimensional arrays, or tensors, is a fundamental operation in computer science with applications ranging from data processing to scientific computing. While various methods exist, achieving this rotation in-place (i.e., with O(1) auxiliary space) presents a significant algorithmic challenge. The elegant three-reversal algorithm provides a well-known O(1) space solution for one-dimensional arrays. This paper introduces a generalization of this method to N dimensions, resulting in the \"$2^n+1$ reversal algorithm\". This algorithm achieves in-place tensor rotation with O(1) auxiliary space and a time complexity linear in the number of elements. We provide a formal definition for N-dimensional tensor reversal, present the algorithm with detailed pseudocode, and offer a rigorous proof of its correctness, demonstrating that the pattern observed in one dimension ($2^1+1=3$ reversals) and two dimensions ($2^2+1=5$ reversals) holds for any arbitrary number of dimensions.","short_abstract":"The rotation of multi-dimensional arrays, or tensors, is a fundamental operation in computer science with applications ranging from data processing to scientific computing. While various methods exist, achieving this rotation in-place (i.e., with O(1) auxiliary space) presents a significant algorithmic challenge. The e...","url_abs":"https://arxiv.org/abs/2512.00111","url_pdf":"https://arxiv.org/pdf/2512.00111v1","authors":"[\"Dexin Chen\"]","published":"2025-11-27T13:12:12Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}