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Time Optimization in Speed-Constrained Frechet Distance

Khademhossein, Maryam | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: English
  3. Document No: 46622 (52)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Zarrabi-Zadeh, Hamid Reza
  7. Abstract:
  8. The Frechet distance is a well-known geometric measure for evaluating the similarity of two polygonal curves. This distance is also known as dog-leash distance, as one can intuitively imagine the distance as the minimum length of a leash needed for a person to walk his/her dog, each walking along one of the curves from beginning to the end, without backtracking. The Frechet distance has several applications e.g., in computer graphics, computer vision, handwriting recognition and GIS.
    In the standard denition of the Frechet distance, there is no limit on the speed of the motion on each of the curves. In 2009, Maheshwari et al. introduced a new variant of the Frechet distance in which each segment of the polygonal curves has a lower and upper bound on the speed of motion along that segment. Maheshwari et al. gave an algorithm to nd the Frechet distance between two polygonal curves of length n in O(n log n) time.In this thesis, the following speed-constrained optimization problem is introduced: Given two polygonal curves with speed limits specifying the maximum and minimum speeds al- lowed on each segment of the curves, nd the minimum time for traversing both curves from beginning to the end such that the distance between the two moving objects does not exceed a given distance. The algorithm of Maheshwari et al. for calculating the speed constrained Frechet distance can also be used for the time optimization problem. The time complexity of this algorithm for suggested new problem is O (2nn4n ) . In this thesis, an exact algorithm with O(4nn4 log n) time is proposed to solve the time optimization in speed-constrained Frechet distance
  9. Keywords:
  10. Time Optimization ; Frechet Distance Problem ; Polygonal Curve ; Speed Constrained