JFR: An Efficient Jump Frontier Relaxation Strategy for Bellman-Ford
Xin Wang, Xi Chen
TL;DR
JFR reimagines Bellman–Ford-based shortest-path computation by integrating frontier filtering and bounded multi-hop jump propagation to dramatically reduce relaxation operations while preserving correctness on graphs with negative weights. The framework provides a formal frontier-sufficiency basis and an amortized analysis showing how a k-bounded propagation depth yields substantial operational savings, balanced against LMH overhead. Empirical results—spanning Python verification and large-scale C++ benchmarks—demonstrate robust performance gains across sparse, dense, and adversarial topologies, including ultra-large graphs where relaxations drop by orders of magnitude and wall-clock time is dramatically reduced. The findings suggest JFR as a practical, structure-aware alternative to SPFA variants, with strong potential for high-throughput and energy-conscious applications, and point to future improvements in queue structures, dynamic frontier granularity, and cache-aware implementations.
Abstract
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.