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Algorithms for Path Simplification

Daneshpajouh, Shervin | 2013

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45665 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Ghodsi, Mohammad
  7. Abstract:
  8. In this thesis, we present different algorithms for path simplification. We first study this problem under area measures. We present an approximation algorithm for sum-area measure and an optimal algorithm for diff-area measure. Both of these algorithms can be applied on general paths. Moreover, we study the homotopic path simplification. We present a general framework for path simplification which work for desired error measure. We first present a strongly homotopic simplification algorithm for x-monotone paths. Also, we study the strongly homotopic simplification for general paths. We present a geometric tree data structure and present an algorithm based on this data structure. Furthermore, we present a homotopic simplification algorithm for general paths. To our knowledge, these two algorithms are the first optimal algorithms for general paths. For the case in which the running time is an issue, we present a heuristic method. Moreover, we study the path simplification under visibility measures. We first study this problem under the size of the weak visibility polygon and present an algorithm for max-error of the path. We prove that the simplification problem under the area of the weak visibility polygon and for sum-error of the path is NP-hard. We present an approximation algorithm for this problem
  9. Keywords:
  10. Computational Geometry ; Line Simplification ; Algorithm ; Visibility Algorithm ; Homotopy Theory

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