Efficient piecewise-linear function approximation using the uniform metric

Abstract

We given anO(n logn)-time method for finding a bestk-link piecewise-linear function approximating ann-point planar point set using the well-known uniform metric to measure the error, ε≥0, of the approximation. Our methods is based upon new characterizations of such functions, which we exploit to design an efficient algorithm using a plane sweep in “ε space” followed by several applications of the parametric-searching technique. The previous best running time for this problems wasO(n 2).

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This research was announced in preliminary form at the 10th ACM Symposium on Computational Geometry. The author was partially supported by the NSF and DARPA under Grant CCR-8908092, and by the NSF under Grants IRI-9116843 and CCR-9300079.

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Goodrich, M.T. Efficient piecewise-linear function approximation using the uniform metric. Discrete & Computational Geometry 14, 445–462 (1995). https://doi.org/10.1007/BF02570717

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Keywords

  • Computational Geometry
  • Binary Search
  • Simple Polygon
  • Geodesic Path
  • Polygonal Approximation