A hollow axis-aligned box is the boundary of the cartesian product of d compact intervals in R d. We show that for d ≥ 3, if any 2 d of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any 5 of a collection

Abstract. Let B be any set of n axis-aligned boxes in R d, d ≥ 1. We call a subset N ⊆ B a(1/c)-net for B if any p ∈ R d contained in more than n/c boxes of B must be contained in a box of N, or equivalently if a point not contained in any box in N can only stab at most n/c boxes of B. General VC

We present easy-to-implement incremental algorithms for computing the union of axis-aligned boxes. These algorithms can effectively be used for the implementa-tion of packing algorithms which try to fit differently sized axis aligned boxes into a container modelled as a fixed point cloud. 1

casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axis-aligned boxes). The new scanline-order algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective

Let B be any set of n axis-aligned boxes in R d, d ≥ 1. For any point p, we define the subset Bp of B as Bp = {B ∈ B: p ∈ B}. A box B in Bp is said to be stabbed by p. A subset N ⊆ B is a (1/c)-net

Let B be any set of n axis-aligned boxes in Rd, d ≥ 1. For any point p, we define the subset Bp of B as Bp = {B ∈ B: p ∈ B}. A box B in Bp is said to be stabbed by p. A subset N ⊆ B is a (1/c)-net

this paper: we assume the topology of the network (the bridge graph) is given, and our only task is to place the bridges so as to minimize the dilation

. For n pairwise disjoint disks in R3 and a parameter r ∈ N, we construct a 1 r size O(r2). For n axis-aligned rectangles in R3, we construct a 1 r-cutting of size O(r3/2). As an application related to multi-point location in three-space, we present tight bounds on the cost of spanning trees across

Abstract Given a set of points S ={x 1,...,x m}⊂R n and ɛ>0, we propose and analyze an algorithm for the problem of computing a (1 + ɛ)-approximation to the minimum-volume axis-aligned ellipsoid enclosing S. We establish that our algorithm is polynomial for fixed ɛ. In addition, the algorithm

Given a set of points S = {x 1,..., x m} ⊂ R n and ɛ> 0, we propose and analyze an algorithm for the problem of computing a (1 + ɛ)-approximation to the the minimum volume axis-aligned ellipsoid enclosing S. We establish that our algorithm is polynomial for fixed ɛ. In addition, the algorithm