Dijkstra's Algorithm

# Dijkstra's Algorithm - REPORT DIJKSTRA'S ALGORITHM DONE BY:...

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REPORT DIJKSTRA’S ALGORITHM

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DONE BY: MERIN PUTHUPARAMPIL TOPICS 1. INTRODUCTION 2. DESCRIPTION OF THE ALGORITHM 3. PSEUDO-CODE OF THE ALGORITHM 4. EXAMPLE 5. PROOF OF THE DIJKSTRA’S ALGORITHM 6. EFFICIENCY 7. DIS-ADVANTAGES 8. RELATED ALGORITHMS 9. APPLICATIONS 10.REFERENCES
1. INTRODUCTION Dijkstra's algorithm is called the single-source shortest path. It is also known as the single source shortest path problem. It computes length of the shortest path from the source to each of the remaining vertices in the graph. The single source shortest path problem can be described as follows: Let G= {V, E} be a directed weighted graph with V having the set of vertices. The special vertex s in V, where s is the source and let for any edge e in E, EdgeCost(e) be the length of edge e. All the weights in the graph should be non-negative. Before going in depth about Dijkstra’s algorithm let’s talk in detail about directed-weighted graph. Directed graph can be defined as an ordered pair G: = (V,E) with V is a set, whose elements are called vertices or nodes and E is a set of ordered pairs of vertices, called directed edges, arcs, or arrows. Directed graphs are also known as digraph. Figure: Directed graph

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Directed-weighted graph is a directed graph with weight attached to each of the edge of the graph. Figure: Directed-weighted graph Dijkstra’s –A Greedy Algorithm Greedy algorithms use problem solving methods based on actions to see if there’s a better long term strategy. Dijkstra’s algorithm uses the greedy approach to solve the single source shortest problem. It repeatedly selects from the unselected vertices, vertex v nearest to source s and declares the distance to be the actual shortest distance from s to v. The edges of v are then checked to see if their destination can be reached by v followed by the relevant outgoing edges.
2. DESCRIPTION OF THE ALGORITHM Before going into details of the pseudo-code of the algorithm it is important to know how the algorithm works. Dijkstra’s algorithm works by solving the sub- problem k, which computes the shortest path from the source to vertices among the k closest vertices to the source. For the dijkstra’s algorithm to work it should be directed- weighted graph and the edges should be non-negative. If the edges are negative then the actual shortest path cannot be obtained. At the k th round, there will be a set called Frontier of k vertices that will consist of the vertices closest to the source and the vertices that lie outside frontier are computed and put into New Frontier. The shortest distance obtained is maintained in sDist[w]. It holds the estimate of the distance from s to w. Dijkstra’s algorithm finds the next closest vertex by maintaining the New

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## This note was uploaded on 02/06/2012 for the course FACULTY OF WXGE6320 taught by Professor Noraini during the Winter '09 term at University of Malaya.

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Dijkstra's Algorithm - REPORT DIJKSTRA'S ALGORITHM DONE BY:...

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