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Testing Properties of Geometric Figures

Rajabi, Amir Hossein | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50172 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Abam, Mohammad Ali
  7. Abstract:
  8. In this thesis, we investigate some problems in Sublinear field. We designed an algorithm that approximate the minimum distance of a shape to be a disk. In the first algorithm, we assumed that its input is a matrix and 1s in the matrix represent black pixels and 0s in the matrix represent white pixels. Also, we designed another algorithm that its input is a data structure contains the positions of a convex shape and we can sample uniformly from its pixels. In this problem similar to the first problem we must approximate the minimum distance of a shape to be a disk. Finally, we designed an algorithm for counting disks in a matrix. The input is a matrix that it contains some disks which have the same radius. In the algorithm, we approximate the number of disks
  9. Keywords:
  10. Computational Geometry ; Randomized Algorithm ; Property Testing ; SubLine Algorithms ; Diskable Property

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