A Delaunay tetrahedralization of n vertices is exhibited for which a straight line can pass through the interiors of Θ(n) tetrahedra. This solves an open problem of Nina Amenta, who asked whether a line can stab more than O(n) tetrahedra. The construction generalizes to higher dimensions: in d dimensions, a line can stab the interiors of Θ(ndd/2e) Delaunay d-simplices. The relationship between ...

Let S be a set of n points in R, and let r be a parameter with 1 6 r 6 n. A rectilinear r-partition for S is a collection Ψ(S) := {(S1, b1), . . . , (St, bt)}, such that the sets Si form a partition of S, each bi is the bounding box of Si, and n/2r 6 |Si| 6 2n/r for all 1 6 i 6 t. The (rectilinear) stabbing number of Ψ(S) is the maximum number of bounding boxes in Ψ(S) that are intersected by a...

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. Sin...

The occurrence of stabbing headaches in children requires a thorough diagnostic approach that excludes secondary headaches. The organic background should be taken into consideration when alarming symptoms occur, such as a purely 1-sided location, a change in the character of the headache, or possibly a link to physical activity. The current study describes the case of an 8-year-old girl who suf...

The occurrence of stabbing headaches in children requires a thorough diagnostic approach that excludes secondary headaches. The organic background should be taken into consideration when alarming symptoms occur, such as a purely 1-sided location, a change in the character of the headache, or possibly a link to physical activity. The current study describes the case of an 8-year-old girl who suf...

The occurrence of stabbing headaches in children requires a thorough diagnostic approach that excludes secondary headaches. The organic background should be taken into consideration when alarming symptoms occur, such as a purely 1-sided location, a change in the character of the headache, or possibly a link to physical activity. The current study describes the case of an 8-year-old girl who suf...

92 1 Lansche RK: Ophthalmodynia periodica. Headache 1964; 4: 247–249. 2 Headache Classifi cation Subcommittee of the International Headache Society: The international classifi cation of headache disorders. Cephalalgia 2004; 24(suppl 1):1–151. 3 Raskin NH, Schwartz RK: Icepick-like pain. Neurology 1980; 30: 203– 205. 4 Pareja JA, Ruiz J, De Isla C, Al-Sabbah H, Espejo J: Idiopathic stabbing head...

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the or...