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Finding vertices of Dual LI(2) Systems

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Summary
Objective
To implement a method of finding vertices of dual LI(2) systems by exploiting the graphical structure
of the bases
This report aims to explain what a dual LI(2) system is, why a new method of exploiting the graphical
structure of the bases of LP problems is going to be considered, how the method of implementing a
new algorithm is to be carried out, and in conclusion, find out whether or not it is successful.

Contents
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 What is a Dual LI(2) System? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 What is a graph? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 What is Vertex Enumeration? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 What is Degeneracy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 The Problem 5
2.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 EnumerateVertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 SOLVE (G,w,x) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 CREATEBFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Design and Implementation 12
3.1 Language selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Class Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4 Code Framework and Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Time Management 16
4.1 Proposed Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 Revisions to the Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5 Results and Testing 18
5.1 Running the code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 Test Plans for the code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
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6 Conclusion and Evaluation 22
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6.1.1 Minimum requirements and Extensions . . . . . . . . . . . . . . . . . . . . . 22
6.1.2 Problems encountered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6.1.3 What could have been done differently? . . . . . . . . . . . . . . . . . . . . . 23
6.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.2.1 Did the Program enhance the current solutions? . . . . . . . . . . . . . . . . . 24
6.2.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Bibliography 26
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