Dijkstra Shortest Path Algorithm Implementation in MATLAB (ShortestPath_Djk)

Implementing shortest path algorithms in MATLAB is crucial for graph theory applications and path planning. Dijkstra's algorithm, as one of the classical shortest path algorithms, is particularly suitable for solving single-source shortest path problems in weighted directed or undirected graphs.

The implementation approach of ShortestPath_Djk follows these key steps: Initialization: Create an adjacency matrix representation of the graph and initialize distance and visited node arrays. The code typically uses MATLAB's matrix operations for efficient initialization. Source Selection: Set the source node with distance 0 to itself, while assigning infinite values (commonly represented by Inf in MATLAB) to all other nodes. Iterative Computation: Among unvisited nodes, select the node with the minimum current distance using MATLAB's min() function, then update the shortest distances to its neighboring nodes through vectorized operations. Termination Condition: The algorithm concludes when all reachable nodes have been visited or when the shortest paths are determined, which can be efficiently monitored using logical indexing.

The MATLAB implementation can leverage sparse matrix storage for adjacency relationships to enhance computational efficiency, especially beneficial when handling large-scale graphs. For substantial datasets, priority queue optimization using MATLAB's min-heap implementation can reduce the complexity of finding minimum-distance nodes from O(V²) to O(E + V log V).

Dijkstra's algorithm finds applications in path planning, network routing optimization, and transportation systems. However, for graphs with negative weight edges, alternative algorithms such as Bellman-Ford should be considered, as Dijkstra's algorithm requires non-negative edge weights to guarantee optimal solutions.