A Bottom-Up Algorithm for Negative-Weight SSSP with Integrated Negative Cycle Finding

TL;DR

This paper introduces a simplified, practical algorithm for Negative-Weight SSSP that integrates negative cycle detection, emphasizing clarity and robustness over theoretical efficiency.

Contribution

The paper presents a simplified algorithm that combines negative cycle detection with SSSP solving, improving clarity and robustness compared to previous methods.

Findings

Fully integrated negative cycle finding into the SSSP algorithm

Uses graph diameter as a recursive parameter for robustness

Simplifies implementation and analysis of negative-weight SSSP

Abstract

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.