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Preprocessing 2D data for fast convex hull computations.

Oswaldo Cadenas1, Graham M Megson2

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This study introduces a method to reduce 2D point sets for faster convex hull computations. The technique preserves the convex hull while significantly decreasing the number of points, achieving over 90% reduction and doubling computation speed.

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Area of Science:

  • Computational Geometry
  • Computer Science

Background:

  • Convex hull algorithms are fundamental in computational geometry.
  • Efficient computation of convex hulls is crucial for various applications.
  • Existing methods may face performance challenges with large datasets.

Purpose of the Study:

  • To present a novel method for reducing the size of 2D point sets.
  • To ensure the reduced set maintains the same convex hull as the original set.
  • To enhance the efficiency of convex hull computation through data reduction.

Main Methods:

  • Developing a preprocessing algorithm to reduce n 2D points to s points.
  • The method is applicable to 2D points represented as real numbers.
  • Experimental validation on four datasets to assess reduction efficacy.

Main Results:

  • Achieved point reduction percentages exceeding 90% across datasets.
  • Demonstrated significant acceleration in convex hull computations.
  • Speedup factors of at least two were observed for common convex hull algorithms.

Conclusions:

  • The proposed reduction method is theoretically O(n), making it an efficient preprocessing step.
  • The technique effectively reduces data size while preserving essential geometric properties.
  • This approach is suitable for optimizing convex hull algorithms on large 2D datasets.