An Improved Dijkstra’s Shortest Path Algorithm for Sparse Networks
This technical research paper investigates an improved version of Dijkstra’s shortest path algorithm for sparse weighted networks. Traditional implementations of Dijkstra’s algorithm can achieve a time complexity of O(m + n log n) when Fibonacci heaps are used, but the authors argue that heap construction increases implementation complexity. The proposed approach modifies the original algorithm so that heap construction is avoided while maintaining competitive performance on sparse graphs. An_improved_Dijkstra’s_shortest… The study focuses on the single-source shortest path problem in weighted directed graphs with non-negative edge lengths. It begins by reviewing a refined Dijkstra algorithm in which each vertex maintains a distance label representing an upper bound on the shortest distance from the source vertex. The main computational bottleneck is repeatedly identifying the unvisited vertex with the smallest distance label. A naïve implementation requires O(n²) time, while Fibonacci-heap implementations improve efficiency but introduce additional implementation complexity. An_improved_Dijkstra’s_shortest… An_improved_Dijkstra’s_shortest… The authors propose an improved Dijkstra algorithm that maintains distance labels in an ordered list. When a distance label changes, the corresponding entry is reinserted into the appropriate location rather than rebuilding or maintaining a heap. The algorithm exploits the characteristics of sparse networks, where each vertex is connected to only a relatively small number of edges. This is particularly relevant to road networks, where the maximum degree of each node is typically low. An_improved_Dijkstra’s_shortest… To support efficient reinsertion, the paper introduces a predefined step-size vector and a binary-search-style process for locating the correct insertion position. This approach reduces the number of comparisons required while avoiding the division operations commonly associated with standard binary search implementations. An_improved_Dijkstra’s_shortest… An_improved_Dijkstra’s_shortest… The theoretical analysis shows that the proposed method requires approximately O(m + Dmax log(n!)) comparisons and arithmetic operations, where m represents the number of edges and Dmax is the maximum number of edges incident on a vertex. The authors argue that this complexity makes the approach especially suitable for large-scale sparse networks where the maximum node degree remains relatively small. An_improved_Dijkstra’s_shortest… An_improved_Dijkstra’s_shortest… The algorithm is evaluated through numerical experiments implemented in MATLAB. Two families of randomly generated sparse networks are tested, with network sizes ranging from approximately 10,000 to 21,000 nodes. The first experiment uses a maximum node degree of four, while the second uses a maximum degree of six. Experimental ratios reported in the paper remain close to the theoretical complexity estimate as network size increases. An_improved_Dijkstra’s_shortest… The paper concludes that the improved Dijkstra approach is practical for large sparse networks, particularly road-traffic networks. By avoiding Fibonacci-heap construction and using an ordered-list reinsertion strategy, the algorithm aims to simplify implementation while maintaining competitive computational performance for shortest-path calculations. An_improved_Dijkstra’s_shortest… Important: because this is a published journal article rather than a university assignment brief, fields such as module name, assessment level and assignment word count are not stated in the source. For the portal, it is safer to use Not specified / Not applicable for those fields rather than inventing academic-assessment details.
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