Uniformly Discrete Forests with Poor Visibility

Noga Alon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ-1-o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlierestimates of Peres, of Solomon and Weiss, and of Adiceam.

Original languageEnglish
Pages (from-to)442-448
Number of pages7
JournalCombinatorics Probability and Computing
Issue number4
StatePublished - 1 Jul 2018


FundersFunder number
Fund for Mathematics
Israeli I-Core
USA-Israeli BSF
USA–Israeli BSF2012/107
Iowa Science Foundation620/13
Israel Science Foundation


    Dive into the research topics of 'Uniformly Discrete Forests with Poor Visibility'. Together they form a unique fingerprint.

    Cite this