TY - GEN
T1 - The distance 4-sector of two points is unique
AU - Fraser, Robert
AU - He, Meng
AU - Kawamura, Akitoshi
AU - López-Ortiz, Alejandro
AU - Munro, J. Ian
AU - Nicholson, Patrick K.
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84893412922&partnerID=8YFLogxK
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U2 - 10.1007/978-3-642-45030-3_57
DO - 10.1007/978-3-642-45030-3_57
M3 - Conference contribution
AN - SCOPUS:84893412922
SN - 9783642450297
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 612
EP - 622
BT - Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings
T2 - 24th International Symposium on Algorithms and Computation, ISAAC 2013
Y2 - 16 December 2013 through 18 December 2013
ER -