Empirical Time Complexity of Generic Dijkstra Algorithm

TL;DR

This paper analyzes the time complexity of the novel Generic Dijkstra algorithm, revealing its quadratic growth with vertices and providing an open-source implementation that confirms its superior performance over existing algorithms.

Contribution

It offers the first independent analysis of Generic Dijkstra's time complexity and provides an open-source implementation validating its efficiency.

Findings

Time complexity grows quadratically with graph vertices.

Peak runtime occurs at approximately 0.25 network utilization.

Generic Dijkstra is about 2.3 times faster than Filtered Graphs algorithm.

Abstract

Generic Dijkstra is a novel algorithm for finding the optimal shortest path in both wavelength-division multiplexed networks (WDM) and elastic optical networks (EON), claimed to outperform known algorithms considerably. Because of its novelty, it has not been independently implemented and verified. Its time complexity also remains unknown. In this paper, we perform run-time analysis and show that Generic Dijkstra running time grows quadratically with the number of graph vertices and logarithmically with the number of edge units. We also discover that the running time of the Generic Dijkstra algorithm in the function of network utilization is not monotonic, as peak running time is at approximately 0.25 network utilization. Additionally, we provide an independent open source implementation of Generic Dijkstra in the Python language. We confirm the correctness of the algorithm and its superior performance. In comparison to the Filtered Graphs algorithm, Generic Dijkstra is approximately 2.3 times faster in networks with 25 to 500 nodes, and in 90% of calls its computation takes less time.