A Performance Comparison of Shortest Path Algorithms in Directed Graphs
Fatima I. Sapundzhi, Kristiyan Danev, Antonina Ivanova, Metodi S. Popstoilov, Slavi G. Georgiev · 2025
This study examines the performance characteristics of four commonly used short-path algorithms, including Dijkstra, Bellman–Ford, Floyd–Warshall, and Dantzig, on randomly generated directed graphs. We analyze theoretical computational complexity and empirical execution time using a custom-built testing framework. The experimental results demonstrate significant performance differences across varying graph densities and sizes, with Dijkstra’s algorithm showing superior performance for sparse graphs while Floyd–Warshall and Dantzig provide more consistent performance for dense graphs. Time complexity analysis confirms the theoretical expectations: Dijkstra’s algorithm performs best on sparse graphs with O (E + V log V) complexity, Bellman–Ford shows O (V · E) complexity suitable for graphs with negative edges, while Floyd–Warshall and Dantzig both demonstrate O(V3) complexity that becomes efficient for dense graphs. This research provides practical insights for algorithm selection based on specific graph properties, guiding developers and researchers in choosing the most efficient algorithm for their particular graph structure requirements.