TY - JOUR

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

AU - Raz, Orit E.

AU - Roche-Newton, Oliver

AU - Sharir, Micha

N1 - Publisher Copyright:
© 2015 Elsevier B.V.

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

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AN - SCOPUS:84926631337

SN - 0012-365X

VL - 338

SP - 1484

EP - 1492

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 8

ER -