JFR: An Efficient Jump Frontier Relaxation Strategy for Bellman-Ford

We propose JFR, a Bellman-Ford-based optimization framework leveraging frontier contraction and abstract multi-hop jump propagation to accelerate shortest-path computation while strictly preserving correctness. JFR achieves substantial reductions in relaxation operations, ranging from -31 to 99 percent, across sparse, dense, and negative-edge graphs, ensuring robust performance even under adversarial or highly connected topologies. On ultra-large graphs with up to N=10,000 nodes and 55,000,000 edges, JFR maintains strong operational reductions and comparable or improved runtime relative to SPFA-SLF, demonstrating consistent robustness across graph size and density. Lower relaxation counts imply reduced memory-access overheads and computational effort; this normalized work reduction highlights JFR's suitability for scenarios requiring high throughput or energy-conscious operation. Future work focuses on integrating high-performance queue structures, adaptive frontier strategies, and cache-aware techniques to further reduce constant-factor overheads and fully realize JFR's practical runtime potential.