Dijkstra's Algorithm and Floyd's Algorithm: MATLAB Implementations

This article discusses the MATLAB implementation of Dijkstra's algorithm and Floyd's algorithm, both of which are used to solve shortest path problems. First, let's understand what the shortest path problem entails. The shortest path problem involves finding the path with the minimum total edge weight between two nodes in a graph. This problem is highly prevalent in various applications, such as determining the shortest route between two locations in navigation systems or finding the fastest path between two devices in communication networks. Dijkstra's algorithm is particularly efficient for single-source shortest path problems, especially when implemented with priority queues to achieve O(E + V log V) time complexity. Key implementation aspects include maintaining a distance array and using a min-heap structure for optimal node selection. Floyd's algorithm, also known as Floyd-Warshall algorithm, solves all-pairs shortest path problems through dynamic programming with O(V³) time complexity. The core implementation involves initializing a distance matrix and iteratively updating it using intermediate nodes. In this article, we will provide detailed explanations of both algorithms' implementation processes, including code structure, key MATLAB functions like graph representation and matrix operations, and practical considerations for handling different graph types. We aim to provide readers with comprehensive guidance for implementing these classic algorithms in MATLAB environments.