The distance 4-sector of two points is unique

Robert Fraser, Meng He, Akitoshi Kawamura, Alejandro López-Ortiz, J. Ian Munro, Patrick K. Nicholson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings
Number of pages11
Publication statusPublished - 2013
Externally publishedYes
Event24th International Symposium on Algorithms and Computation, ISAAC 2013 - Hong Kong, China
Duration: Dec 16 2013Dec 18 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8283 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other24th International Symposium on Algorithms and Computation, ISAAC 2013
CityHong Kong

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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