Project assignment

Determing the most efficient way

to connect the network

Tom von Hegedus, Jochem Lentz, George Karlos,

Zakaria Nafid, Mike Spadaru,

Group 4c

Understand the problem

We have 2 problems:

• Total weight of the initial graph

• Total weight of the Minmumspanningtree

• initial weight – minimumspannigtree

weight = the solution

What do we have?

• A text document with a lot of numbers

• We know that the weighted graph has 40

vertices.

• So we need a 40x40 matrix

Import

Import["C:\\Users\\Tom\\Documents\\network.txt"]

WeightedAdjacencyGraph

• Replace all the – with ∞

• Make 40 lines with 40 numbers

WeightedAdjacencyGraph

WeightedAdjacencyGraph

WeightedAdjacency Matrix

• WeightedAdjacencyMatrix[m] // MatrixForm

• VertexList[m];

TableForm

[Normal@WeightedAdjacencyMatrix[m],

TableHeadings®{c=Style[#,Blue]&/@%,c}]

Initial Graph Weight

• The weight of the initial graph is 261,832

MinimumSpanningTree• Problems with Mathematica

• We used Prims algorithm on table by hand

Wrong !!!

Prims Algorithm

Minimum Spanning Tree

Weight

• The Weight of the Minimumspanningtree

is 2153

Solution

• Initial Graph Weight –

MinimumSpanningTree Weight = solution

• 261,832 – 2153= 259,679

Problems

• The only problem was to get a

MinimumSpanningTree in Mathematica

Solution strategies/ Algorithms/

tools

• Divide the problem into sub problems

• Prim’s Algorithm

• We used the site of Mathematica a lot

Time spent on problem

• About 20 to 25 hours per person.

Conclusion

• Not very hard project

• Problems with MinimumSpanningTree[]

function in Mathematica

Thank you!