TY - JOUR
T1 - Selecting heavily covered points
AU - Chazelle, Bernard
AU - Edelsbrunner, Herbert
AU - Guibas, Leonidas J.
AU - Hershberger, John E.
AU - Seidel, Raimund
AU - Sharir, Micha
PY - 1994
Y1 - 1994
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0028752729&partnerID=8YFLogxK
U2 - 10.1137/S0097539790179919
DO - 10.1137/S0097539790179919
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AN - SCOPUS:0028752729
SN - 0097-5397
VL - 23
SP - 1138
EP - 1151
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 6
ER -