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Computing polygonal path simplification under area measures

Daneshpajouh, S ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.gmod.2012.04.006
  3. Publisher: 2012
  4. Abstract:
  5. In this paper, we consider the restricted version of the well-known 2D line simplification problem under area measures and for restricted version. We first propose a unified definition for both of sum-area and difference-area measures that can be used on a general path of n vertices. The optimal simplification runs in O(n 3) under both of these measures. Under sum-area measure and for a realistic input path, we propose an approximation algorithm of O n2 time complexity to find a simplification of the input path, where is the absolute error of this algorithm compared to the optimal solution. Furthermore, for difference-area measure, we present an algorithm that finds the optimal simplification in O(n 2) time. The best previous results work only on x-monotone paths while both of our algorithms work on general paths. To the best of our knowledge, the results presented here are the first sub-cubic simplification algorithms on these measures for general paths
  6. Keywords:
  7. Linear model simplification ; Absolute error ; Area difference ; Line simplification ; Model simplification ; Optimal solutions ; Polygonal path ; Simplification algorithms ; Time complexity ; Approximation algorithms ; Computational geometry ; Algorithm ; Geometry ; Graphical method ; Linearity ; Numerical model ; Optimization ; Path analysis ; Two-dimensional modeling
  8. Source: Graphical Models ; Volume 74, Issue 5 , September , 2012 , Pages 283-289 ; 15240703 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S1524070312000264