Loading...

Convex Hull Problem in the Uncertain Models

Valoubian, Erfan | 2023

64 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56504 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Ghodsi, Mohammad
  7. Abstract:
  8. Many geometric problems have algorithms that exist on paper for them, such as the Convex Hull problem [1], Minimum Spanning Tree [2], Voronoi Diagram [3], Closest Pair of Points [4], Largest Empty Circle [5], Smallest Enclosing Circle [6], and more. In all of these problems, the assumption is that a certain number of points are given as input, and we must perform various operations on these points based on the nature of the problem. Furthermore, a stronger assumption is that these points are given to us precisely, but in reality, this is not the case, and for various reasons, it is not possible to determine the exact locations of these points. Therefore, it can be said that we are dealing with uncertainty. In this research, we specifically examined the Convex Hull problem, which is one of the most important and fundamental geometric problems. This problem had been under discussion for years with no optimal algorithm for its solution until Kirkpatrick and Seidel [1] presented an optimal algorithm in 1986. However, ten years later, Timothy Chan introduced a much simpler optimal method [7]. Today, the Chan algorithm is considered the optimal approach for this problem. Although this problem has been solved in the case of precise data, many challenges remain when dealing with uncertain data, and it has not been proven that the proposed algorithms are optimal in many cases. In this study, we attempted to review various sources and provide a comprehensive report on the subject.
  9. Keywords:
  10. Computational Geometry ; Uncertainty ; Convex Hull ; Imprecise Data ; Uncertainty Modeling

 Digital Object List