Efficient and Perfect domination on circular-arc graphs

Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$. An \emph{efficient dominating set} is a perfect dominating set $V'$ where $V'$ is also an independent set. These problems are usually posed in terms of edges instead of vertices. Both problems, either for the vertex or edge variant, remains NP-Hard, even when restricted to certain graphs families. We study both variants of the problems for the circular-arc graphs, and show efficient algorithms for all of them

Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree

Graphs can effectively model biomolecules, computer systems, and other applications. A weighted graph is a graph in which values or labels are assigned to the edges of the graph. However, in this thesis, we assign values to the vertices of the graph rather than the edges and we modify several standard graphical measures to incorporate these vertex weights. In particular, we designate the degree of each vertex as its weight. Previous research has not investigated weighting vertices by degree. We find the vertex weighted domination number in connected graphs, beginning with trees, and we define how weighted vertices can affect eccentricity, independence number, and connectivity

The Parametric Aircraft Noise Analysis Module - status overview and recent applications

The German Aerospace Center (DLR) is investigating aircraft noise prediction and noise reduction capabilities. The Parametric Aircraft Noise Analysis Module (PANAM) is a fast prediction tool by the DLR Institute of Aerodynamics and Flow Technology to address overall aircraft noise. It was initially developed to (1) enable comparative design studies with respect to overall aircraft ground noise and to (2) indentify promising low-noise technologies at early aircraft design stages. A brief survey of available and established fast noise prediction codes is provided in order to rank and classify PANAM among existing tools. PANAM predicts aircraft noise generated during arbitrary 3D approach and take-off flight procedures. Noise generation of an operating aircraft is determined by its design, the relative observer position, configuration settings, and operating condition along the flight path. Feasible noise analysis requires a detailed simulation of all these dominating effects. Major aircraft noise components are simulated with individual models and interactions are neglected. Each component is simulated with a separate semi-empirical and parametric noise source model. These models capture major physical effects and correlations yet allow for fast and accurate noise prediction. Sound propagation and convection effects are applied to the emitting noise source in order to transfer static emission into aircraft ground noise impact with respect to the actual flight operating conditions. Recent developments and process interfaces are presented and prediction results are compared with experimental data recorded during DLR flyover noise campaigns with an Airbus A319 (2006), a VFW-614 (2009), and a Boeing B737-700 (2010). Overall, dominating airframe and engine noise sources are adequately modeled and overall aircraft ground noise levels can sufficiently be predicted. The paper concludes with a brief overview on current code applications towards selected noise reduction technologies

An exploration of graph algorithms and graph databases

With data becoming larger in quantity, the need for complex, efficient algorithms to solve computationally complex problems has become greater. In this thesis we evaluate a selection of graph algorithms; we provide a novel algorithm for solving and approximating the Longest Simple Cycle problem, as well as providing novel implementations of other graph algorithms in graph database systems.The first area of exploration is finding the Longest Simple Cycle in a graph problem. We propose two methods of finding the longest simple cycle. The first method is an exact approach based on a flow-based Integer Linear Program. The second is a multi-start local search heuristic which uses a simple depth-first search as a basis for a cycle, and improves this with four perturbation operators.Secondly, we focus on implementing the Minimum Dominating Set problem into graph database systems. An unoptimised greedy heuristic solution to the Minimum Dominating Set problem is implemented into a client-server system using a declarative query language, an embedded database system using an imperative query language and a high level language as a direct comparison. The performance of the graph back-end on the database systems is evaluated. The language expressiveness of the query languages is also explored. We identify limitations of the query methods of the database system, and propose a function that increases the functionality of the queries

Online Learning with Feedback Graphs: Beyond Bandits

We study a general class of online learning problems where the feedback is specified by a graph. This class includes online prediction with expert advice and the multi-armed bandit problem, but also several learning problems where the online player does not necessarily observe his own loss. We analyze how the structure of the feedback graph controls the inherent difficulty of the induced $T$-round learning problem. Specifically, we show that any feedback graph belongs to one of three classes: strongly observable graphs, weakly observable graphs, and unobservable graphs. We prove that the first class induces learning problems with $\widetilde\Theta(\alpha^{1/2} T^{1/2})$ minimax regret, where $\alpha$ is the independence number of the underlying graph; the second class induces problems with $\widetilde\Theta(\delta^{1/3}T^{2/3})$ minimax regret, where $\delta$ is the domination number of a certain portion of the graph; and the third class induces problems with linear minimax regret. Our results subsume much of the previous work on learning with feedback graphs and reveal new connections to partial monitoring games. We also show how the regret is affected if the graphs are allowed to vary with time