An Improved Bellman-Ford Algorithm Based on SPFA

Abstract

In this paper, we proposed an efficient algorithm based on SPFA(shortest path faster algorithm), which is an improved the Bellman-Ford algorithm. The Bellman-Ford algorithm can be used on graphs with negative edge weights unlike Dijkstra's algorithm. And SPFA algorithm used a queue to store the nodes, to avoid redundancy, though the Bellman-Ford algorithm takes a long time to update the nodes table. In this improved algorithm, an adjacency list is also used to store each vertex of the graph, applying dynamic optimal approach. And a queue is used to store the data. The improved algorithm can find the optimal path by continuous relaxation operation to the new node. Simulations to compare the efficiencies for Dijkstra's algorithm, SPFA algorithm and improved Bellman-Ford were taken. The result shows that Dijkstra's algorithm, SPFA algorithm have almost same efficiency on the random graphs, the improved algorithm, although the improved algorithm is not desirable, on grid maps the proposed algorithm is very efficient. The proposed algorithm has reduced two-third times processing time than SPFA algorithm.