# quantitative methods minimal spanning tree and dijkstra

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- 1. MINIMAL- SPANNING TREETechnique to connect all the points of a network whileminimizing the distance between them.Input: Fully connected graph with distances known between the nodes.Output: Tree which gives minimum distance that connectsall the nodes.BITS Pilani, Pilani Campus

2. MINIMAL- SPANNING TREEAlgorithm:1. Select any node in the network2. Connect this node to the nearest node that minimizes total distance.3. Find and connect the nearest node that is not connected. In case of tie, select arbitrary and proceed.4. Repeat step 3 until all nodes are connected. BITS Pilani, Pilani Campus 3. Minimal Spanning Tree-Problem Launderdale Construction Company, Which is currently developing a luxurious housing project in Panama city beach, Florida. Melvin Launderdale, owner and president of Lauderdale Construction, must determine the least expensive way to provide water and power to each house. The network of the House is given in the figure.BITS Pilani, Pilani Campus 4. Each number depicts- Dist ance in hundreds of feetProblem : 5 4 3 5 7 2 3 7 3 2 3 2 3 8 2 1 1 5 6 6 4 BITS Pilani, Pilani Campus 5. MINIMAL- SPANNING TREESolution:5 435723732323 82 1156 64BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956 6. Application of MinimalSpanning TreeNetwork design. Telephone, electrical, hydraulic, TV cable, computer,roadPhone network design Problems-Business with several offices ,Lease phone lines to connect them up with each other,Phone company charges different amounts of money toconnect different pairs of cities.Set of lines that connects all your offices with a minimumtotal cost.- Spanning tree, since if a network isnt a tree youcan always remove some edges and save moneyBITS Pilani, Pilani Campus 7. DIJKSTRA ALGORITHMA graph search algorithm that solves the single-sourceshortest path problem.Input: fully connected graph with distances known betweenthe nodes.Output: For a source node in the graph, the algorithm findsthe path with lowest cost between that vertex and everyother vertex.Can also be used for finding costs of shortest paths from asingle vertex to a single destination BITS Pilani, Pilani Campus 8. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 9. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 10. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 11. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 12. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 13. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 14. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 15. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 16. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 17. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 18. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 19. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 20. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 21. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 22. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 23. DIJKSTRA ALGORITHM BITS Pilani, Pilani Campus 24. References1.) http://optlab- server.sce.carleton.ca/POAnimations2007/DijkstrasAlgo. html2.) Wikipedia.org3.) http://www.cs.princeton.edu/~rs/AlgsDS07/14MST.pdf BITS Pilani, Pilani Campus