Piercing random boxes

Abstract. Consider a set of n random axis parallel boxes in the unit hypercube in Rd , 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 Ωd( √ n(log n)d/2−1) and at most Od( √ n(log n)d/2−1 log log n).

• Type: Journal
• Year: 2011
• Where: RSA
• Authors: Linh V. Tran
• Keywords: Minimum Number, Parallel Boxes, RSA 2011, Unit Hypercube