Sets with few distinct distances do not have heavy lines

Orit E. Raz; Oliver Roche-Newton; Micha Sharir

doi:10.1016/j.disc.2015.02.009

Sets with few distinct distances do not have heavy lines

Orit E. Raz^*, Oliver Roche-Newton, Micha Sharir

^*Corresponding author for this work

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

12 Scopus citations

Abstract

Let P be a set of n points in the plane that determines at most n/5 distinct distances. We show that no line can contain more than O(n43^/52polylog(n)) points of P. We also show a similar result for rectangular distances, equivalent to distances in the Minkowski plane, where the distance between a pair of points is the area of the axis-parallel rectangle that they span.

Original language	English
Pages (from-to)	1484-1492
Number of pages	9
Journal	Discrete Mathematics
Volume	338
Issue number	8
DOIs	https://doi.org/10.1016/j.disc.2015.02.009
State	Published - 6 Aug 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

Distinct distances
Incidences

Access to Document

10.1016/j.disc.2015.02.009

Cite this

@article{6eaaa5250a224fe3aef839775665a7eb,

title = "Sets with few distinct distances do not have heavy lines",

abstract = "Let P be a set of n points in the plane that determines at most n/5 distinct distances. We show that no line can contain more than O(n43/52polylog(n)) points of P. We also show a similar result for rectangular distances, equivalent to distances in the Minkowski plane, where the distance between a pair of points is the area of the axis-parallel rectangle that they span.",

keywords = "Distinct distances, Incidences",

author = "Raz, {Orit E.} and Oliver Roche-Newton and Micha Sharir",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

year = "2015",

month = aug,

day = "6",

doi = "10.1016/j.disc.2015.02.009",

language = "אנגלית",

volume = "338",

pages = "1484--1492",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "8",

}

TY - JOUR

T1 - Sets with few distinct distances do not have heavy lines

AU - Raz, Orit E.

AU - Roche-Newton, Oliver

AU - Sharir, Micha

PY - 2015/8/6

Y1 - 2015/8/6

N2 - Let P be a set of n points in the plane that determines at most n/5 distinct distances. We show that no line can contain more than O(n43/52polylog(n)) points of P. We also show a similar result for rectangular distances, equivalent to distances in the Minkowski plane, where the distance between a pair of points is the area of the axis-parallel rectangle that they span.

AB - Let P be a set of n points in the plane that determines at most n/5 distinct distances. We show that no line can contain more than O(n43/52polylog(n)) points of P. We also show a similar result for rectangular distances, equivalent to distances in the Minkowski plane, where the distance between a pair of points is the area of the axis-parallel rectangle that they span.

KW - Distinct distances

KW - Incidences

UR - http://www.scopus.com/inward/record.url?scp=84926631337&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2015.02.009

DO - 10.1016/j.disc.2015.02.009

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84926631337

SN - 0012-365X

VL - 338

SP - 1484

EP - 1492

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 8

ER -

Sets with few distinct distances do not have heavy lines

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this