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Visibility Testing of Uncertain Segments

Hosseinpour, Hamed | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48835 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Ghodsi, Mohammad
  7. Abstract:
  8. Evaluating the enviroment for achieving efcient kwnoledge in order to justifed environment recognition and making decision based on data analysis is proponed in many felds.One of these problems is Visibility Problem. The Recieved data from real world as input, for visibility problem, is uncertain such that the recieving data of two different measurments will be different with high probability. Therefore, we defne the goal of this research to solving the visibility problem conditioned to that objects or segments are uncertain.Consider ”S” as a set of ”n” uncertain segments in plane. Each uncertain segment locates in two certain places and with probability 1 2 in each place, the goal is to answer the testing visibility problem of a specifc segment (VTUS) that in a nutshell for n given uncertain segments in plane, we are looking forward to computing the probability of visibility of a specifc segment and a given point is plane. A point p and segment s are visible if and only if there is at least one point q on segment s such that p and q are visible. Two point are visible if there is no object as a visiblility barrier that intersects the connected segment from ”p” to ”q”.The complexity of problem has not been revealed, yet. By assuming that solving the problem in polynomial time is impossible, at the frst some solutions are presented then an algorithm for computing the visibility probability is explained that for 1 ⩽ k ⩽ n with O(k) storage in O(nd+1) running time with error of e−Θ( k n 2 ) approximates the answer of problem such that d = min(k + 1; n 2 ). At the end, an FPRAS is illustrated for VTUS problem,too
  9. Keywords:
  10. Computational Geometry ; Visibility Algorithm ; Approximate Algorithm ; Counting Theory ; Uncertain Segments

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