Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

The Acute Retinal Necrosis Syndrome

The acute retinal necrosis syndrome is characterized by necrotizing retinitis, vitritis, and retinal vasculitis occurring in otherwise healthy patients. Experience with 11 cases and the review of 30 additional cases in the literature are presented. In this series, 50% of the affected eyes developed retinal detachments, and 64% had a final visual acuity of less than 20/200. The natural history, diagnosis, postulated etiology, and suggestions for management will be discussed