Quantitative methods minimal spanning tree and dijkstra [compatibility mode]
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Transcript of Quantitative methods minimal spanning tree and dijkstra [compatibility mode]
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BITS Pilani, Pilani Campus
Technique to connect all the points of a network while minimizing the distance between them.
Input: Fully connected graph with distances known between the nodes.
Output: Tree which gives minimum distance that connects all the nodes.
MINIMAL- SPANNING TREE
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BITS Pilani, Pilani Campus
Algorithm:
1. Select any node in the network
2. Connect this node to the nearest node that minimizestotal distance.
3. Find and connect the nearest node that is notconnected. In case of tie, select arbitrary and proceed.
4. Repeat step 3 until all nodes are connected.
MINIMAL- SPANNING TREE
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BITS Pilani, Pilani Campus
Launderdale Construction Company, Which is currentlydeveloping a luxurious housing project in Panama citybeach, Florida.
Melvin Launderdale, owner and president of LauderdaleConstruction, must determine the least expensive way toprovide water and power to each house.
The network of the House is given in the figure.
Minimal Spanning Tree-Problem
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BITS Pilani, Pilani Campus
Problem :
Each number depicts-Dist ance in hundreds of feet
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BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956
MINIMAL- SPANNING TREE
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Solution:
2
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BITS Pilani, Pilani Campus
Network design.– Telephone, electrical, hydraulic, TV cable, computer, road
Phone network design Problems-
Business with several offices ,
Lease phone lines to connect them up with each other,
Phone company charges different amounts of money to connect different pairs of cities.
Set of lines that connects all your offices with a minimum total cost.
- Spanning tree, since if a network isn’t a tree you can always remove some edges and save money
Application of Minimal Spanning Tree
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BITS Pilani, Pilani Campus
A graph search algorithm that solves the single-source shortest path problem.
Input: fully connected graph with distances known between the nodes.
Output: For a source node in the graph, the algorithm finds the path with lowest cost between that vertex and every other vertex.
Can also be used for finding costs of shortest paths from a single vertex to a single destination
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
DIJKSTRA ALGORITHM
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BITS Pilani, Pilani Campus
1.) http://optlab-server.sce.carleton.ca/POAnimations2007/DijkstrasAlgo.html
2.) Wikipedia.org
3.) http://www.cs.princeton.edu/~rs/AlgsDS07/14MST.pdf
References