Single Source Shortest Paths in Randomized Two-Dimensional Mesh Networks

Abstract

The Single Source Shortest Path (SSSP) problem focuses on finding the shortest paths from a source vertex to all other vertices in a graph. This problem is crucial in various domains, including transportation, telecommunications and urban planning. Although Dijkstra's algorithm is effective for solving the SSSP in general cases, in some special cases, such as two-dimensional mesh networks (2DMN), its performance is not satisfactory. To address this limitation, this paper presents an improved approach, i.e., the row-by-row dynamic programming (RRDP) algorithm, which is specifically optimized for 2DMNs and can significantly reduce computation times, although in worst case the complexity of RRDP is higher than Dijkstra's algorithm. We tested the RRDP algorithm against the traditional Dijkstra's algorithm using the same 2DMN instances, and found that RRDP runs much faster than Dijkstra's algorithm on most instances. This innovation offers new insights and practical solutions for improving path planning algorithms in grid network environments.