On 2-site voronoi diagrams under geometric distance functions

Gill Barequet; Matthew Dickerson; David Eppstein; David Hodorkovsky; Kira Vyatkina

doi:https://doi.org/10.1007/s11390-013-1328-2

On 2-site voronoi diagrams under geometric distance functions

Gill Barequet, Matthew Dickerson, David Eppstein, David Hodorkovsky, Kira Vyatkina

Computer Science

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We revisit a new type of Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest- and furthest-neighbor 2-site Voronoi diagrams of a point set in the plane with respect to these distance functions. In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter.

Original language	English
Pages (from-to)	267-277
Number of pages	11
Journal	Journal of Computer Science and Technology
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s11390-013-1328-2
State	Published - Mar 2013

Keywords

Davenport-Schinzel theory
crossing-number lemma
distance function
lower envelope

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science
Hardware and Architecture
Computer Science Applications
Computational Theory and Mathematics

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https://doi.org/10.1007/s11390-013-1328-2

Cite this

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title = "On 2-site voronoi diagrams under geometric distance functions",

abstract = "We revisit a new type of Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest- and furthest-neighbor 2-site Voronoi diagrams of a point set in the plane with respect to these distance functions. In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter.",

keywords = "Davenport-Schinzel theory, crossing-number lemma, distance function, lower envelope",

author = "Gill Barequet and Matthew Dickerson and David Eppstein and David Hodorkovsky and Kira Vyatkina",

note = "Funding Information: Regular Paper David Eppstein was supported by National Science Foundation of USA under Grants Nos. 0830403 and 1217322 and US Office of Naval Research under Grant No. N00014-08-1-1015. ①Obviously, ◦(v,p,q) ∕ C(v,p,q) if any of the three points is properly contained in the circle whose diameter is defined by the two other points. {\textcopyright}2013 Springer Science + Business Media, LLC & Science Press, China",

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doi = "https://doi.org/10.1007/s11390-013-1328-2",

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AU - Barequet, Gill

AU - Dickerson, Matthew

AU - Eppstein, David

AU - Hodorkovsky, David

AU - Vyatkina, Kira

N1 - Funding Information: Regular Paper David Eppstein was supported by National Science Foundation of USA under Grants Nos. 0830403 and 1217322 and US Office of Naval Research under Grant No. N00014-08-1-1015. ①Obviously, ◦(v,p,q) ∕ C(v,p,q) if any of the three points is properly contained in the circle whose diameter is defined by the two other points. ©2013 Springer Science + Business Media, LLC & Science Press, China

PY - 2013/3

Y1 - 2013/3

N2 - We revisit a new type of Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest- and furthest-neighbor 2-site Voronoi diagrams of a point set in the plane with respect to these distance functions. In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter.

AB - We revisit a new type of Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest- and furthest-neighbor 2-site Voronoi diagrams of a point set in the plane with respect to these distance functions. In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter.

KW - Davenport-Schinzel theory

KW - crossing-number lemma

KW - distance function

KW - lower envelope

UR - http://www.scopus.com/inward/record.url?scp=84879620723&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s11390-013-1328-2

DO - https://doi.org/10.1007/s11390-013-1328-2

M3 - مقالة

SN - 1000-9000

VL - 28

SP - 267

EP - 277

JO - Journal of Computer Science and Technology

JF - Journal of Computer Science and Technology

IS - 2

ER -

On 2-site voronoi diagrams under geometric distance functions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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