Fast Stabbing of Boxes in High Dimensions

We present in this paper a simple yet e cient algorithm for stabbing a set S of n axisparallel boxes in d-dimensional space with c(S) points in output-sensitive time O(dn log c(S)) and linear space. Let c (S) and b (S) be, respectively, the minimum number of points required to stab S and the maximum number of pairwise disjoint boxes of S. We prove that b (S)6c (S)6c(S)6b (S)(1+log2 b (S))d-1 . Since

• Type: Conference
• Year: 1996
• Where: CCCG
• Authors: Frank Nielsen
• Keywords: Algorithm, CCCG 1996, CCCG 2007, Pairwise Disjoint Boxes, Stabbing