A New Algorithm to Compute Single Source Shortest Path in a Real Edge Weighted Graph to Optimize Time Complexity

A prime concern of a Shortest-Path problem is to handle any real edge weight values whether it is positive or negative with the feature of negative weight cycle detection if exists. Number of single source shortest-path algorithms are available that can handle negative weight cycle, where the most stable algorithm till date executes with polynomial time complexity. In this paper, an algorithm is proposed for graphs with real edge weights to solve single source shortest path problem with the feature of negative weight cycle detection in order to optimize time complexity. The time complexity analysis and proof of correctness confirmed that, for graph with identical configuration, the proposed algorithm provides faster and accurate solutions with quasilinear time complexity than the existing algorithm that comes out with the same solution with a polynomial time complexity.