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# Dijkstra’S Algorithm

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Method used by ArcGIS Network Analysis

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### Dijkstra’S Algorithm

1. 1. DIJKSTRA’s ALGORITHM<br />Dijkstra_Algorithm<br />AmanArora<br />Geographical Analyst<br />Lepton Software<br />Mail Id: aman.arora@leptonmaps.com<br />aman.july07@gmail.com<br />
2. 2. Introduction<br />Dijkstra's Algorithm derived by a Dutch computer scientist ‘EdsgerDijkstra’ in 1956 and published in 1959.<br />It’s a graph search algorithm that solves the single-source shortest path problem for a graph with nonnegative edge path costs, producing a shortest path tree. <br />This algorithm is often used in routing and as a subroutine in other graph algorithms.<br />
3. 3. How it works ?<br />This algorithm finds the path with lowest cost (i.e. the shortest path) between that vertex and every other vertex. For example, if the vertices of the graph represent cities and edge path costs represent driving distances between pairs of cities connected by a direct road, Dijkstra's algorithm can be used to find the shortest route between one city and all other cities.<br />According to this algorithm, to solve a given problem, we need to solve different parts of problems.<br />
4. 4. Numerical Algorithm<br />Formulae<br /> O(|V|²+|E|) = O(|V|²) <br />Where,<br />E= Edges, V= Vertices <br />|E| = Function of Edges<br />|V| = Function of Vertices and <br /> O = Constant<br />
5. 5. Graph Algorithm <br />In this interconnected ‘Vertex’ we’ll use ‘Dijkstra’s Algorithm’.<br />To use this algorithm in this network we have to start from a decided vertex and then continue to others.<br />
6. 6. Graph Algorithm <br />So, for the calculation give infinite value to all Vertex. <br />And start with ‘A’ using this table:<br />
7. 7. Graph Algorithm <br />
8. 8. Graph Algorithm <br />
9. 9. Graph Algorithm <br />
10. 10. Graph Algorithm <br />
11. 11. Graph Algorithm <br />
12. 12. Graph Algorithm <br />
13. 13. Graph Algorithm <br />
14. 14. Graph Algorithm<br />So with this ‘Graph Algorithm’ we found our best lowest cost route in this interconnected Vertex.<br />And the best lowest cost path is given below:<br /> A B F C D (H) G<br />So total cost from ‘A’ to ‘G’ vertex is ‘70’ which is lowest cost from other Vertex. <br />
15. 15. What is the analysis technique using this Algorithm in ArcGIS Network Analysis?<br />From this demonstration now we know about method used by this algorithm to find out lowest cost route.<br />Exactly this technique is adapted by ArcGIS NA and it uses to find out solution of any network problem.<br />Where we use Vertex to reach our destination, in ArcGIS NA we use junctions as Vertex to find out lowest cost route, New Service area, closest facility etc.<br />
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