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)

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.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings
Pages612-622
Number of pages11
DOIs
Publication statusPublished - Dec 1 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

Other

Other24th International Symposium on Algorithms and Computation, ISAAC 2013
CountryChina
CityHong Kong
Period12/16/1312/18/13

Fingerprint

Sector
Uniqueness
Bisector
Parabola
Euclidean plane
Simplicity
Line
Generalization
Concepts

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Fraser, R., He, M., Kawamura, A., López-Ortiz, A., Munro, J. I., & Nicholson, P. K. (2013). The distance 4-sector of two points is unique. In Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings (pp. 612-622). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8283 LNCS). https://doi.org/10.1007/978-3-642-45030-3_57

The distance 4-sector of two points is unique. / Fraser, Robert; He, Meng; Kawamura, Akitoshi; López-Ortiz, Alejandro; Munro, J. Ian; Nicholson, Patrick K.

Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. 2013. p. 612-622 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8283 LNCS).

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

Fraser, R, He, M, Kawamura, A, López-Ortiz, A, Munro, JI & Nicholson, PK 2013, The distance 4-sector of two points is unique. in Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8283 LNCS, pp. 612-622, 24th International Symposium on Algorithms and Computation, ISAAC 2013, Hong Kong, China, 12/16/13. https://doi.org/10.1007/978-3-642-45030-3_57
Fraser R, He M, Kawamura A, López-Ortiz A, Munro JI, Nicholson PK. The distance 4-sector of two points is unique. In Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. 2013. p. 612-622. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-45030-3_57
Fraser, Robert ; He, Meng ; Kawamura, Akitoshi ; López-Ortiz, Alejandro ; Munro, J. Ian ; Nicholson, Patrick K. / The distance 4-sector of two points is unique. Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. 2013. pp. 612-622 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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