Finding the Shortest Path using Dijkstra’s Algorithm

Abstract

Graph theory is one of the most important branches of discrete mathematics which is a study of graphs which are mathematical structures that are used to model pair wise relations between objects. Many discrete problems can be analysed using graph theoretic models. Graph theory plays prominent role in computer science and logistics management. The main application of graph theory is to find the shortest path problems, optimal assignment problems, time tabling problems, travelling salesman problems. Roads plays an important role as every day people from various cities, states and villages has to travel to work, schools, business and to transport the goods. In the roadway networks finding the shortest paths between various locations is the major problem. Because of this problem many shortest path algorithms are developed. In roadway network applications finding shortest path is important in city emergency handling as finding the shortest path is important to save the life and drive guiding systems to reduce the travel time, simultaneously to reduce the cost of implementation. The shortest path problem is to find the path between to vertices on a given graph, such that the sum of the weigths on its constituent edges is minimized. In this paper for a Dijkstra's algorithm gives a solution for a single source shortest path problems. In this algorithm the shortest path is calculated for a whole network starting from a source vertex (or) initial vertex by finding the upper bound of the distance between two vertices can be calculated in advance on the given transportation network.