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Line Transversals to Disjoint Balls

✍ Scribed by Ciprian Borcea; Xavier Goaoc; Sylvain Petitjean

Publisher
Springer
Year
2007
Tongue
English
Weight
565 KB
Volume
39
Category
Article
ISSN
0179-5376

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Let F n denote a family of disjoint n balls in R d (d 2), and let \*=\*(F n ) denote the ratio (maximum radius)Γ‚(minimum radius) among the balls in F n . We prove that (1) there is a unit vector uÁ such that every line parallel to uÁ intersects at most O(-(1+log \*) n log n) balls of F n , and (2) t