The Remote-Clique Problem Revisited

Given a positive integer k and a complete graph with non-negative edge weights that satisfy the triangle inequality, the remote-clique problem is to find a subset of k vertices having a maximum-weight induced subgraph. A greedy algorithm for the problem has been shown to have an approximation ratio of 4, but this analysis was not shown to be tight. In this thesis, we present an algorithm called d-Greedy Augment that generalizes this greedy algorithm (they are equivalent when d = 1). We use the technique of factor-revealing linear programs to prove that d-Greedy Augment, which has a running time of O(kdnd ), achieves an approximation ratio of (2k ? 2)/(k + d ? 2). Thus, when d = 1, d-Greedy Augment achieves an approximation ratio of 2 and runs in time O(kn), making it the fastest known 2-approximation for the remote-clique problem. Beyond proving this worst-case result, we also examine the behavior of d-Greedy Augment in practice. First, we provide some theoretical results regarding the expected case performance of d-Greedy Augment on random graphs, and second, we describe data from some experiments that test the performance of d-Greedy Augment and related heuristics

The Good Old Davis-Putnam Procedure Helps Counting Models

As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(nm^d), where d=-1/log(1-p). The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas

Trapped atoms in cavity QED: coupling quantized light and matter

On the occasion of the hundredth anniversary of Albert Einstein's annus mirabilis, we reflect on the development and current state of research in cavity quantum electrodynamics in the optical domain. Cavity QED is a field which undeniably traces its origins to Einstein's seminal work on the statistical theory of light and the nature of its quantized interaction with matter. In this paper, we emphasize the development of techniques for the confinement of atoms strongly coupled to high-finesse resonators and the experiments which these techniques enable

Cavity QED with Single Atoms and Photons

Recent experimental advances in the field of cavity quantum electrodynamics (QED) have opened new possibilities for control of atom-photon interactions. A laser with "one and the same atom" demonstrates the theory of laser operation pressed to its conceptual limit. The generation of single photons on demand and the realization of cavity QED with well defined atomic numbers N = 0, 1, 2,... both represent important steps toward realizing diverse protocols in quantum information science. Coherent manipulation of the atomic state via Raman transitions provides a new tool in cavity QED for in situ monitoring and control of the atom-cavity system. All of these achievements share a common point of departure: the regime of strong coupling. It is thus interesting to consider briefly the history of the strong coupling criterion in cavity QED and to trace out the path that research has taken in the pursuit of this goal

Grundversorgung: Der Weg aus der Krise führt auch über die MPA

Die meisten Hausärzte und Hausärztinnen in der Schweiz sind dauerhaft überlastet. Um zusätzliche Kapazitäten zu schaffen, sind ihre Leistungen auf mehr Schultern zu verteilen und die Betreuung im (Praxis-)Team zu verstärken. Besonders dafür geeignet ist die Begleitung von chronisch kranken Patienten durch die Medizinische Praxisassistentin. Das Problem: Der Arzt kann diese Leistungen nicht abrechnen. Dies ist so rasch wie möglich zu ändern, damit die MPA endlich den Wert erhält, den sie längst verdient