TY - GEN

T1 - On regular vertices on the union of planar objects

AU - Ezra, Esther

AU - Pach, Janos

AU - Sharir, Micha

PY - 2007

Y1 - 2007

N2 - Let C be a collection of n compact convex sets in the plane, such that the boundaries of any pair of sets in C intersect in at most s points, for some constant s. We show that the maximum number of regular vertices (intersection points of two boundaries that intersect twice) on the boundary of the union U of C is O*(n4/3), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.

AB - Let C be a collection of n compact convex sets in the plane, such that the boundaries of any pair of sets in C intersect in at most s points, for some constant s. We show that the maximum number of regular vertices (intersection points of two boundaries that intersect twice) on the boundary of the union U of C is O*(n4/3), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.

KW - (1/r)-cuttings

KW - Regular vertices

KW - Union of geometric objects

UR - http://www.scopus.com/inward/record.url?scp=35348867384&partnerID=8YFLogxK

U2 - 10.1145/1247069.1247110

DO - 10.1145/1247069.1247110

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AN - SCOPUS:35348867384

SN - 1595937056

SN - 9781595937056

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 220

EP - 226

BT - Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07

T2 - 23rd Annual Symposium on Computational Geometry, SCG'07

Y2 - 6 June 2007 through 8 June 2007

ER -