The graph model is used widely for representing connected objects within a specific area. These objects are defined as nodes; where the connection is represented as arc called edges. The shortest path between two nodes is one of the most focus researchers' attentions. Many algorithms are developed with different structured approach for reducing the shortest path cost. The most widely used algorithm is Dijkstra algorithm. This algorithm has been represented with various structural developments in order to reduce the shortest path cost. This paper highlights the idea of using a storage medium to store the solution path from Dijkstra algorithm, then, uses it to find the implicit path in an ideal time cost. The performance of Dijkstra algorithm using an appropriate data structure is improved. Our results emphasize that the searching time through the given data structure is reduced within different graphs models.

The shortest path between two points is one of the greatest challenges facing the researchers nowadays. There are many algorithms and mechanisms that are designed and still all according to the certain approach and adopted structural. The most famous and widely used algorithm is Dijkstra algorithm, which is characterized by finding the shortest path between two points through graph data structure. It's obvious to find the implicit path from the solution path; but the searching time varies according to the type of data structure used to store the solution path. This paper improves the development of Dijkstra algorithm using linked hash map data structure for storing the produced solution shortest path, and then investigates the subsequent implicit paths within this data structure. The result show that the searching time through the given data structure is much better than restart the algorithm again to search for the same path.

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