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Quantitative methods minimal spanning tree and dijkstra [compatibility mode]
1. MINIMAL- SPANNING TREE
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.
BITS Pilani, Pilani Campus
2. MINIMAL- SPANNING TREE
Algorithm:
1. Select any node in the network
2. 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 feet
Problem :
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 TREE
Solution:
5 4
3
5 7
2
3 7
3 2
3
2
3 8
2 1
1
5
6 6
4
BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956
6. Application of Minimal
Spanning Tree
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
BITS Pilani, Pilani Campus
7. DIJKSTRA ALGORITHM
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
BITS Pilani, Pilani Campus
