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 journalArticlepeer-review

12 Scopus citations


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 languageEnglish
Pages (from-to)1484-1492
Number of pages9
JournalDiscrete Mathematics
Issue number8
StatePublished - 6 Aug 2015


FundersFunder number
Austrian Science Fund
Austrian Science FundF5511-N26
National Science Foundation
Israeli Centers for Research Excellence4/11
United States-Israel Binational Science Foundation
Israel Science Foundation2012/229
Hermann Minkowski-MINERVA Center for Geometry
Tel Aviv University


    • Distinct distances
    • Incidences


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