Selecting heavily covered points

Bernard Chazelle*, Herbert Edelsbrunner, Leonidas J. Guibas, John E. Hershberger, Raimund Seidel, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A collection of geometric selection lemmas is proved, such as the following: For any set P of n points in three-dimensional space and any set S of m spheres, where each sphere passes through a distinct point pair in P. there exists a point x, not necessarily in P, that is enclosed by Ω(m2/(n2 log6 n2/m)) of the spheres in S. Similar results apply in arbitrary fixed dimensions, and for geometric bodies other than spheres. The results have applications in reducing the size of geometric structures, such as three-dimensional Delaunay triangulations and Gabriel graphs, by adding extra points to their defining sets.

Original languageEnglish
Pages (from-to)1138-1151
Number of pages14
JournalSIAM Journal on Computing
Issue number6
StatePublished - 1994
Externally publishedYes


Dive into the research topics of 'Selecting heavily covered points'. Together they form a unique fingerprint.

Cite this