A refined search tree technique for Dominating Set on planar graphs

We establish a refined search tree technique for the parameterized DOMINATING SET problem on planar graphs. Here, we are given an undirected graph and we ask for a set of at most k vertices such that every other vertex has at least one neighbor in this set. We describe algorithms with running times O(8^kn) and O(8^kk+n³), where n is the number of vertices in the graph, based on bounded search trees. We describe a set of polynomial time data-reduction rules for a more general “annotated” problem on black/white graphs that asks for a set of k vertices (black or white) that dominate all the black vertices. An intricate argument based on the Euler formula then establishes an efficient branching strategy for reduced inputs to this problem. In addition, we give a family examples showing that the bound of the branching theorem is optimal with respect to our reduction rules. Our final search tree algorithm is easy to implement; its analysis, however, is involved.     

The Geometric Dilation of Finite Point Sets

Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclidean distance. The supremum of all these ratios is called the geometric dilation of G. Given a finite point set, we would like to know the smallest possible dilation of any graph that contains the given points. In this paper we prove that a dilation of 1.678 is always sufficient, and that π/2 = 1.570... is sometimes necessary in order to accommodate a finite set of points.     

A Case Study in Periodic Timetabling

In the overwhelming majority of public transportation companies, designing a periodic timetable is even nowadays largely performed manually. Software tools only support the planners in evaluating a periodic timetable, or by letting them comfortably shift sets of trips by some minutes, but they rarely use optimization methods. One of the main arguments against optimization is that there is no clear objective in practice, but that many criteria such as amount of rolling stock required, average passenger changing time, average speed of the trains, and the number of cross-wise correspondences have to be considered.This case study will demonstrate on the example of the Berlin underground (BVG) that all these goals can be met if carefully modeled, and that timetables constructed by optimization lead to considerable improvements.Our approach uses the Periodic Event Scheduling Problem (PESP) with several add-ons concerning problem reduction and strengthening. The resulting integer linear programs are solved with the CPLEX MIP-Solver. We have been able to construct periodic timetables that improve the current timetable considerably. For any of the above criteria, we have been able to identify global lower and upper bounds. Our favorite timetable improves the current BVG timetable in each of these criteria.     

An interactive data management system for river water quality data

Water quality data banks are needed to document the status and trends of water pollution in a country. Examples of such systems are the STORET system in the U.S., the NAQUADAT system in Canada and the EIS system in Scandinavia. All of these systems require trained personnel to help in the formulation of the inquiry and the actual querying of the system.By contrast, what is described in this paper is an on-line, interactive data management and analysis system which allows the user the direct search, update, retrieval and analysis of the data from a computer terminal. The user addresses the system in a high level language closely resembling English and has complete control over building, updating and querying the individual data banks. Almost all statistical operations can be performed on the data starting from histograms, distributions, correlations to regression, discriminant, component and spectral analysis. Commands for producing camera-ready graphs on graphic terminals are available.The system is implemented on The University of Michigan Computer System and can be accessed through local telephone numbers in more than 100 cities in the U.S. and Canada and from the major European capitals via the TELENET system. The operation of the system is illustrated on a small sample data base on the Ohio river provided by the Ohio River Sanitation Commission (ORSANCO).     

Thermische Gestaltänderung von Arbeitswalzen und ihre Ausnutzung zur Beeinflussung der Planheit von kaltgewalztem Band

Planheit von Kaltband. Kühlung und/oder Erwärmung einer Arbeitswalze, induktive Walzenerwärmung. Temperaturfelder in der Arbeitswalze, zugeordnete Wärmedehnung.     

Electronic Simulation of the Vertebrate Retina

An electronic analog model of a section of the vertebrate retina has been constructed. It is structured in 5 layers of cells corresponding to the structure of the natural retina, whereby the function and connections of the single cell models can be varied. While signal processing occurs in the first four layers by evaluating several timedependent slow potentials as positive or negative, impulse rate time functions are emitted from the ganglion cells at the retina output. Various neural networks as inputs for the 25 Ganglion cells can be realized by using various patchboard connections. Several examples for simulation results are presented which closely fit comparable neurophysiological findings.     

Significance of low water—solid ratio and temperature on the physico-mechanical characteristics of hydrates of tricalcium aluminate

Hydration characteristics are reported of tricalcium aluminate studied at 20 and 80 °C using water-solid ratios of 0.2 and 1.0. Hydration products were subjected to differential thermal analysis, thermogravimetric analysis, scanning electron microscopy, length change, porosity and pore size distribution, and micro-hardness measurements. Hydration proceeds faster at 80 °C than at 20 °C and the cubic C₃AH₆ phase is detected in the first few seconds. At 20 °C hydration occurs with the initial formation of the hexagonal phases and expansion is continuous. At higher temperatures and a water-solid ratio of 0.2, after an initial small expansion, the dimensional change is low. The product at 80 °C develops more than fourfold the hardness value developed at 20 °C. After 2 days of hydration, porosity, per cent C₃AH₆ and microhardness are 15.2%, 83% and 38.9 kg/mm²; corresponding values for the product obtained at 20 °C are 21.5%, 75% and 9.1 kg/mm². Microstructural examination of the material formed at 80 °C indicates a closely welded and continuous network of the cubic phase. These results reveal that at a low water-solid ratio and higher temperatures the formation of the cubic phase from C₃A results in an enhancement of strength.     

Compact stacking of diode lasers for pulsed light sources of high brightness

A compact stacking architecture for high-power diode-laser arrays is proposed and compared with traditional stacks. The objective of compact stacking is to achieve high brightness values without the use of microlenses. The calculated brightness for a compact stack is over 300 W mm(-2) sr(-1), which is approximately 40 times higher than that of a traditional stack made of similar laser emitters. Even higher brightness values of over 600 W mm(-2) sr(-1) were reached in practice. A laser head was manufactured in which the light from several compact laser stacks could be fiber coupled or the light could be transformed to a highly uniform beam.