We introduce and develop a new semi-algebraic proof system, called Stabbing Planes that is in the style of DPLL-based modern SAT solvers. As with DPLL, there is only one rule: the current polytope can be subdivided by branching on an inequality and its “integer negation.” That is, we can (nondeterministically choose) a hyperplane ax ≥ b with integer coefficients, which partitions the polytope i...

The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner et al. We provide efficient algorithms for the following problems: computing the stabbing wedges for S, finding a stabbing wedge for a set of parallel segments with equal length, and computing other stabbers for S such as a double-wedge and a zigzag. The time and space ...

Stab-resistant body armour is now becoming a standard item of equipment for police officers in the United Kingdom. In the UK these are usually required to have a stab resistance as specified by the Police Scientific Development Branch KR42 standard [G. Parker, PSDB Stab Resistant Body Armour Test Procedure, Police Scientific Development Branch, Publication No 10/93, 1993]. There are several oth...

Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel segment inside P . We present a 3-approximation algorithm for finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms.

The stabbing number of a geometric structure in IR with respect to lines is the maximum number of times any line stabs (intersects) the structure. We present algorithms for constructing popular geometric data structures with small stabbing number and for computing lower bounds on an optimal solution. We evaluate our methods experimentally.

In the weighted rectangle stabbing problem we are given a grid in ]R2 consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption that each rectangle is intersected by at least one column and at least one row. The objective is...

A linear time algorithm for minimum link paths inside a simple polygon. Algorithms for the reduction of the number of points required to represent a line or its caricature. Computing the visibility polygon from a convex set and related problems. implementation of the Douglas-Peucker line simpli-cation algorithm using at most cn log n operations. In preparation, 1991. 16] H. Imai and M. Iri. Com...

o bjective: to explain an important  aspect of violence, the spatiotemporal pattern of trauma in victims of violence visited in emergency room of rajaei hospital, shiraz, iran m e thods: this cross-sectional prospective study comprised 109 randomly selected victims of violence visited in emergency room of rajaei hospital, a tertiary referral hospital affiliated to shiraz university of medical s...

We develop several linear or near-linear space and I/Oefficient dynamic data structures for orthogonal range-max queries and stabbing-max queries. Given a set of N weighted points in R, the rangemax problem asks for the maximum-weight point in a query hyperrectangle. In the dual stabbing-max problem, we are given N weighted hyper-rectangles, and we wish to find the maximum-weight rectangle cont...