We present a lock-free implementation of Dijkstra's shortest-path algorithm that employs a Fibonacci heap priority queue in the Rust programming language. The design preserves sequential consistency across concurrent enqueue and extract-min operations by leveraging atomic reference counting and weak pointers. We formally prove that the heap maintains the heap property and that the overall algorithm achieves the classic O(|E|+|V|log|V|) asymptotic bound when executed on a single logical thread. Static abstract syntax tree inspection confirms that the implementation contains 305 lines of code and 21 function blocks, with all heap nodes allocated in a contiguous vector to avoid pointer indirection overhead. No empirical wall-clock measurements are reported; the analysis is purely theoretical and verified by automated AST tooling.
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_19_dijkstra_shortest_path_with_fibonac,
title={Concurrent Lock-Free Dijkstra Shortest Path with Fibonacci Heap Priority Queue in ...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-19_dijkstra_shortest_path_with_fibonac/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-19_dijkstra_shortest_path_with_fibonac/2026-10-19_dijkstra_shortest_path_with_fibonac.pdf}}
}