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Table of Contents:

Chapter 1: Introduction
– Background of the Study
– Problem Statement
– Research Questions
– Importance of the Study

Chapter 2: Literature Review
– Overview of Combinatorial Geometry
– Convex Hulls
– Voronoi Diagrams
– Previous Studies on Convex Hulls and Voronoi Diagrams

Chapter 3: Research Methodology
– Research Design
– Data Collection Methods
– Data Analysis Techniques
– Sampling Methods

Chapter 4: Discussion of Findings
– Analysis of Convex Hulls and Voronoi Diagrams
– Comparison of Different Approaches
– Implications of Findings

Chapter 5: Conclusion and Summary
– Summary of Findings
– Conclusion
– Recommendations for Future Research

Brief Overview:

The thesis on Combinatorial Geometry: Convex Hulls and Voronoi Diagrams aims to explore the applications and properties of convex hulls and Voronoi diagrams in combinatorial geometry. The study will investigate the theoretical background of these geometric constructs, as well as their practical implications in various fields such as computer science, robotics, and geography.

Chapter one provides an introduction to the research topic, outlining the background of the study, problem statement, research questions, and the importance of the study. Chapter two delves into a comprehensive literature review, covering the basics of combinatorial geometry, convex hulls, Voronoi diagrams, and previous studies in the field.

Chapter three describes the research methodology, detailing the research design, data collection methods, data analysis techniques, and sampling methods employed in the study. Chapter four presents a discussion of the findings, analyzing the properties of convex hulls and Voronoi diagrams, comparing different approaches, and discussing the implications of the findings.

Lastly, chapter five offers a conclusion and summary of the thesis, summarizing the key findings, drawing conclusions, and providing recommendations for future research in the field of combinatorial geometry. Overall, this thesis seeks to contribute to the existing body of knowledge on convex hulls and Voronoi diagrams, highlighting their significance in various disciplines and paving the way for further research in this area.

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