Time and Memory Trade-Offs in Shortest-Path Algorithms Across Graph Topologies: A*, Bellman–Ford, Dijkstra, AI-Augmented A* and a Neural Baseline

This study presents a comparative evaluation of Dijkstra’s algorithm, A*, Bellman-Ford, AI-Augmented A* and a neural AI-based model for shortest-path computation across diverse graph topologies, with a focus on time efficiency and memory consumption under standardized experimental conditions. We analyzed grids, random graphs, and scale-free graphs of sizes up to 103,103 nodes, specifically examining 100- and 1000-node grids, 100- and 1000-node random graphs, and 100-node scale-free graphs. The algorithms were benchmarked through repeated runs per condition on a server-class system equipped with an Intel Xeon Gold 6248R processor, NVIDIA Tesla V100 GPU (32 GB), 256 GB RAM, and Ubuntu 20.04. A* consistently outperformed Dijkstra’s algorithm when paired with an informative admissible heuristic, exhibiting faster runtimes by approximately 1.37× to 1.91× across various topologies. In comparison, Bellman-Ford was slower than Dijkstra’s by approximately 1.50× to 1.92×, depending on graph type and size; however, it remained a robust option in scenarios involving negative edge weights or when early-termination conditions reduced practical iterations. The AI model demonstrated the slowest performance across conditions, incurring runtimes that were 2.60× to 3.23× higher than A* and 1.62× to 2.15× higher than Bellman-Ford, offering limited gains as a direct solver. These findings underscore topology-sensitive trade-offs: A* is preferred when a suitable heuristic is available; Dijkstra’s serves as a strong baseline in the absence of heuristics; Bellman-Ford is appropriate for handling negative weights; and current AI approaches are not yet competitive for exact shortest paths but may hold promise as learned heuristics to augment A*. We provide environmental details and comparative results to support reproducibility and facilitate further investigation into hybrid learned-classical strategies.