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Piercing random boxes
Author(s) -
Tran Linh V.
Publication year - 2011
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20321
Subject(s) - combinatorics , struct , hypercube , mathematics , omega , infinity , unit (ring theory) , binary logarithm , discrete mathematics , physics , computer science , mathematical analysis , mathematics education , quantum mechanics , programming language
Consider a set of n random axis parallel boxes in the unit hypercube in ${\bf R}^{d}$ , where d is fixed and n tends to infinity. We show that the minimum number of points one needs to pierce all these boxes is, with high probability, at least $\Omega_d(\sqrt{n}(\log n)^{d/2-1})$ and at most $O_d(\sqrt{n}(\log n)^{d/2-1}\log \log n)$ . © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 365–380, 2011
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