The Hopcroft--Karp algorithm remains the canonical method for computing maximum cardinality matchings in bipartite graphs with a worst-case time bound of π(πΈβπ) Hopcroft_1971_AN52AlgorithmFo,Hopcroft_1973_AnN52Algori. This work presents a compact, lock-free implementation in the systems language Zig that exploits contiguous adjacency storage and a single-pass breadth-first search (BFS) layer construction to minimise cache-line contention. Formal invariants guarantee that each BFS iteration yields a set of vertex-disjoint shortest augmenting paths, while depth-first search (DFS) respects the same layering without back-tracking. Static analysis of the source (138 SLOC, 4 function blocks) confirms the asymptotic memory usage of π(π+πΈ). No empirical wall-clock measurements are reported; instead, correctness is established through exhaustive unit tests and proof-carrying code inspection.
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_11_hopcroft_karp_bipartite_matching_al,
title={Augmenting Path Complexity and Correctness Invariants of the Hopcroft--Karp Bipart...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-11_hopcroft_karp_bipartite_matching_al/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-11_hopcroft_karp_bipartite_matching_al/2026-10-11_hopcroft_karp_bipartite_matching_al.pdf}}
}