We present a randomized algorithm that determines, in expectedO(n2) time, whether a line exists that stabs each of a set of oriented convex polygons in R3 with a total of n edges. If a stabbing line exists, the algorithm computes at least one such line. We show that the computation amounts to constructing a convex polytope in R5 and inspecting its edges for intersections with a four-dimensional...

We give a general framework for the problem of finding all minimal hitting sets of a family of objects in R by another. We apply this framework to the following problems: (i) hitting hyper-rectangles by points in R; (ii) stabbing connected objects by axis-parallel hyperplanes in R; and (iii) hitting half-planes by points. For both the covering and hitting set versions, we obtain incremental pol...

Computational complexity is studied for the problem of stabbing set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0 where the set of segments forms a straight line drawing of some connected planar graph. We claim strong NP-hardness of the problem over the class of 4-connected (i.e. Hamiltonian) plane triangulations of bounded vertex degree for small r, ...

Ice pick headache is a momentary, transient, repetitive headache disorder and manifests with the stabbing pains and jolts. The exact mechanism causing this disease is unknown. Premature ventricular contractions are early depolarization of the ventricular myocardium and in the absence of a structural heart disease, it is considered to be a benign disease. In this report, we describe a male patie...

A 50 year old male with obstructive sleep apnea developed de novo, daily, intense, continuous, left side pounding headache with superimposed stabbing pains, fluctuating in severity. Headache was associated with ptosis of the left eye, left hypoglossal palsy and eventual tongue hemiatrophy, in the absence of papilledema. His Brain and neck imaging procedures (MRI, MRA, MRV) and a left temporal a...