The Distance 4-Sector of Two Points Is Unique

  • Robert Fraser
  • Meng He
  • Akitoshi Kawamura
  • Alejandro López-Ortiz
  • J. Ian Munro
  • Patrick K. Nicholson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

Abstract

The (distance) k-sector is a generalization of the concept of bisectors proposed by Asano, Matoušek and Tokuyama. We prove the uniqueness of the 4-sector of two points in the Euclidean plane. Despite the simplicity of the unique 4-sector (which consists of a line and two parabolas), our proof is quite non-trivial. We begin by establishing uniqueness in a small region of the plane, which we show may be perpetually expanded afterward.

Keywords

distance k-sector Tarski fixed point uniqueness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Robert Fraser
    • 1
  • Meng He
    • 2
  • Akitoshi Kawamura
    • 3
  • Alejandro López-Ortiz
    • 4
  • J. Ian Munro
    • 4
  • Patrick K. Nicholson
    • 5
  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCanada
  2. 2.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada
  3. 3.Department of Computer ScienceUniversity of TokyoTokyoJapan
  4. 4.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  5. 5.Max-Planck-Institut für InformatikSaarbrückenGermany

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