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Complexity Analysis for Digital Hyperplane Recognition in Arbitrary Fixed Dimension

  • Valentin E. Brimkov
  • Stefan S. Dantchev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)

Abstract

We consider the following problem. Given a set of points M = {p 1,p 2...p m } ⊆ ℝ n , decide whether M is a portion of a digital hyperplane and, if so, determine its analytical representation. In our setting p 1,p 2...p m may be arbitrary points (possibly, with rational and/or irrational coefficients) and the dimension n may be any arbitrary fixed integer. We provide an algorithm that solves this digital hyperplane recognition problem by reducing it to an integer linear programming problem of fixed dimension within an algebraic model of computation. The algorithm performs O(mlogD) arithmetic operations, where D is a bound on the norm of the domain elements.

Keywords

Digital hyperplane digital plane recognition integer programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Valentin E. Brimkov
    • 1
  • Stefan S. Dantchev
    • 2
  1. 1.Fairmont State UniversityFairmontUSA
  2. 2.Science LabsUniversity of DurhamDurhamEngland

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