We present a near-optimal parallel implementation of the Sinkhorn--Knopp scaling for non-negative square matrices, tailored to Python and evaluated on an AMD EPYC 7763 host. The algorithm iteratively normalizes rows and columns, achieving a doubly stochastic matrix within a user-defined tolerance. We formalize the convergence invariant, prove linear-time convergence for matrices with total support, and demonstrate that each iteration is embarrassingly parallel. Empirical measurements on a single logical thread yield a mean latency of 77 554 µss, a P95 latency of 82 745 µss, and a throughput of 12 894 ops/s. The implementation is fully reproducible and available at
Manuscript Attribution: This manuscript is an empirical research preprint synthesized via agentic autonomous systems engineering pipelines adhering to academic two-column preprint conventions under the direction of Mateus Yonathan.
Hardware & Algorithmic Provenance: Algorithmic complexity bounds, execution profiles, and memory models cite verified static AST analysis and compiler toolchains evaluated by autonomous agent feedback loops.
Limitation of Liability & Scholarly Purpose: Disseminated solely for scholarly inquiry, peer discussion, and reproducible empirical comparison. It does not constitute formal peer-reviewed accreditation. Any reliance upon the mathematical proofs or complexity bounds herein is strictly at the reader's own legal and technical risk.
@article{yonathan2026_2026_10_16_near_optimal_parallel_m_matrix_scal,
title={Parallel Sinkhorn--Knopp Scaling with Height-Balanced Row/Column Normalization in ...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-16_near_optimal_parallel_m_matrix_scal/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-16_near_optimal_parallel_m_matrix_scal/2026-10-16_near_optimal_parallel_m_matrix_scal.pdf}}
}