We present a simplified algorithm for solving the Negative-Weight Single-Source Shortest Paths (SSSP) problem, focusing on enhancing clarity and practicality over prior methods. Our algorithm uses graph diameter as a recursive parameter, offering greater robustness to the properties of the decomposed graph compared to earlier approaches. Additionally, we fully integrate negative-weight cycle finding into the algorithm by augmenting the Bellman-Ford/Dijkstra hybrid, eliminating the need for a separate cycle-finding procedure found in prior methods. Although the algorithm achieves no theoretical efficiency gains, it simplifies negative cycle finding and emphasizes design simplicity, making it more accessible for implementation and analysis. This work highlights the importance of robust parameterization and algorithmic simplicity in addressing the challenges of Negative-Weight SSSP.

翻译：本文提出了一种用于解决负权单源最短路径问题的简化算法，相较于现有方法，该算法更注重提升清晰度与实用性。本算法以图直径作为递归参数，与早期方法相比，对分解图的属性具有更强的鲁棒性。此外，我们通过增强Bellman-Ford/Dijkstra混合策略，将负权环检测完全集成到算法流程中，从而无需采用现有方法中独立的环检测步骤。尽管该算法未实现理论效率的提升，但它简化了负环检测过程并强调设计简洁性，使其更易于实现与分析。本工作凸显了鲁棒参数化与算法简洁性在应对负权单源最短路径挑战中的重要性。