Shortest Path Between Two Nodes on a Potential Railway System In Cyprus

Mr. Erdogan Kaygan(European University of Lefke)

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CONTENTS

– Introduction– Aim Of The Project– Graph Theory– Dijkstra Algorithm – How The System Works( Software)– Conclusion– References

Introduction

•Most common problem in computer science.Most common problem in computer science.

•Shortest path problem is the problem of finding a path between two Shortest path problem is the problem of finding a path between two vertices.vertices.

•Aim of the projectAim of the project: Finding and calculating the shortest way to get : Finding and calculating the shortest way to get from one location to another on a Cyprus railway map.from one location to another on a Cyprus railway map.

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Graph Theory

•Directed Graph Directed Graph Directed graph defined as G = (V,E)Directed graph defined as G = (V,E)

wherewhere;;

V: a set of vertices and V: a set of vertices and

E: a set of edges E: a set of edges

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V1 V2

V3

E1

E2E3

Figure1 Directed Graph

Graph Theory

•Adjacent ListAdjacent List EEach vertex has a list of which vertices it is adjacent toach vertex has a list of which vertices it is adjacent to.. Example:Example:

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V1 V2

V3

E1

E2E3

Vertices Adjacent List

V1 V2, V3

V2 V1, V3

V3 V1, V2Figure2 Directed Graph

Table1. Adjacent List

Dijkstra Algorithm

• Designed to find the shortest path between two nodes.Designed to find the shortest path between two nodes.

•Algorithm stepsAlgorithm steps

1)1) Select current node 0Select current node 0Set the value of all other nodesSet the value of all other nodesto infinity.to infinity.Mark nodes unvisitedMark nodes unvisited

6

10

3

58

72

Girne

Guzelyurt Lefkosa

Akdogan

Gazimagosa

Dijkstra Algorithm

2) Update new value for visited node2) Update new value for visited nodeCheck the smallest.Check the smallest.

Girne-Guzelyurt: 10 Girne-Guzelyurt: 10 Girne-Lefkosa: 5Girne-Lefkosa: 5Girne-Gazimagosa: 8Girne-Gazimagosa: 8

7

10

3

58

72

Girne

Guzelyurt Lefkosa

Akdogan

Gazimagosa

10 5 8

Dijkstra Algorithm

3) For each unvisited nodes (Akdogan )3) For each unvisited nodes (Akdogan )update the values. update the values.

Girne-Lefkosa: 5Girne-Lefkosa: 5Lefkosa-Akdogan: 7Lefkosa-Akdogan: 7Sum: 5+7: 12Sum: 5+7: 12

8

10

3

58

72

Girne

Guzelyurt Lefkosa

Akdogan

Gazimagosa

10 5 8

12

Dijkstra Algorithm

4) Check the values minimum or not4) Check the values minimum or not If not updated again.If not updated again.

Girne-Gazimagosa: 8Girne-Gazimagosa: 8Lefkosa-Akdogan: 2Lefkosa-Akdogan: 2Sum: 8+2: 10Sum: 8+2: 10

9

10

3

58

72

Girne

Guzelyurt Lefkosa

Akdogan

Gazimagosa

10 5 8

10

Dijkstra Algorithm

5)5) Check all nodes are visitedCheck all nodes are visited

Path:Path: Girne-Gazimagosa-AkdoganGirne-Gazimagosa-AkdoganDistance:Distance: 10 10

10

10

3

58

72

Girne

Guzelyurt Lefkosa

Akdogan

Gazimagosa

105 8

10

How The System Works

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Conclusion

•The project gave me a good opportunity to experiment windows The project gave me a good opportunity to experiment windows form programming with C# programming language.form programming with C# programming language.

•I gained a great amount of experience in using the objects of I gained a great amount of experience in using the objects of Graphics classGraphics class..

•This project was a good experiment to turn the theoretical This project was a good experiment to turn the theoretical knowledge into practice.knowledge into practice.

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References

•Thomas A. Standish.”Data Structures, Algorithms, and Software Principles”. Computer Thomas A. Standish.”Data Structures, Algorithms, and Software Principles”. Computer Science Department University of Calfornia,Irvine.ISBN 0-201-52880-0. May 1994.Science Department University of Calfornia,Irvine.ISBN 0-201-52880-0. May 1994.

•http://www.wordiq.com/definition/Dijkstra's_algorithmhttp://www.wordiq.com/definition/Dijkstra's_algorithm

•http://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Graph_theory

•Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001). "Section Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001). "Section 24.3: Dijkstra's algorithm". Introduction to Algorithms (Second ed.). MIT Press and McGraw-Hill. 24.3: Dijkstra's algorithm". Introduction to Algorithms (Second ed.). MIT Press and McGraw-Hill. pp. 595–601. ISBN 0-262-03293-7.pp. 595–601. ISBN 0-262-03293-7.

•http://www.dotnetperls.com/pathfindinghttp://www.dotnetperls.com/pathfinding

•http://en.wikipedia.org/wiki/Dijkstra's_algorithmhttp://en.wikipedia.org/wiki/Dijkstra's_algorithm

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THANK YOU FOR LISTENINGTHANK YOU FOR LISTENING

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