Distributed Approximation Algorithms for the Minimum Dominating Set in K_h-Minor-Free Graphs

In this paper we will give two distributed approximation algorithms (in the Local model) for the minimum dominating set problem. First we will give a distributed algorithm which finds a dominating set D of size O(gamma(G)) in a graph G which has no topological copy of K_h. The algorithm runs L_h rounds where L_h is a constant which depends on h only. This procedure can be used to obtain a distributed algorithm which given epsilon>0 finds in a graph G with no K_h-minor a dominating set D of size at most (1+epsilon)gamma(G). The second algorithm runs in O(log^*{|V(G)|}) rounds

Distributed Distance-rr Dominating Set on Sparse High-Girth Graphs

The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about distance-r domination. This is actually the case for other important closely-related covering problem, namely, the distance-$r$ independent set problem. By result of Kuhn et al. we know the distributed domination problem is hard on high girth graphs; we study the problem on a slightly restricted subclass of these graphs: graphs of bounded expansion with high girth, i.e. their girth should be at least $4r + 3$. We show that in such graphs, for every constant $r$, a simple greedy CONGEST algorithm provides a constant-factor approximation of the minimum distance-$r$ dominating set problem, in a constant number of rounds. More precisely, our constants are dependent to $r$, not to the size of the graph. This is the first algorithm that shows there are non-trivial constant factor approximations in constant number of rounds for any distance $r$-covering problem in distributed settings. To show the dependency on r is inevitable, we provide an unconditional lower bound showing the same problem is hard already on rings. We also show that our analysis of the algorithm is relatively tight, that is any significant improvement to the approximation factor requires new algorithmic ideas

Distributed distance-r covering problems on sparse high-girth graphs

We prove that the distance-r dominating set, distance-r connected dominating set, distance-r vertex cover, and distance-r connected vertex cover problems admit constant factor approximations in the CONGEST model of distributed computing in a constant number of rounds on classes of sparse high-girth graphs. In this paper, sparse means bounded expansion, and high-girth means girth at least 4r + 2. Our algorithm is quite simple; however, the proof of its approximation guarantee is non-trivial. To complement the algorithmic results, we show tightness of our approximation by providing a loosely matching lower bound on rings. Our result is the first to show the existence of constant-factor approximations in a constant number of rounds in non-trivial classes of graphs for distance-r covering problems

Pulse propagation, graph cover, and packet forwarding

We study distributed systems, with a particular focus on graph problems and fault tolerance. Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal by being a distributed system consisting of very simple nodes. We show that even in the typical mode of operation without faults, TRIX performs significantly better than a regular wire or clock tree: Statistical evaluation of our simulated experiments show that we achieve a skew with standard deviation of O(log log H), where H is the height of the TRIX grid. The distance-r generalization of classic graph problems can give us insights on how distance affects hardness of a problem. For the distance-r dominating set problem, we present both an algorithmic upper and unconditional lower bound for any graph class with certain high-girth and sparseness criteria. In particular, our algorithm achieves a O(r·f(r))-approximation in time O(r), where f is the expansion function, which correlates with density. For constant r, this implies a constant approximation factor, in constant time. We also show that no algorithm can achieve a (2r + 1 − δ)-approximation for any δ > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we extend the algorithm to related graph cover problems and even to a different execution model. Furthermore, we investigate the problem of packet forwarding, which addresses the question of how and when best to forward packets in a distributed system. These packets are injected by an adversary. We build on the existing algorithm OED to handle more than a single destination. In particular, we show that buffers of size O(log n) are sufficient for this algorithm, in contrast to O(n) for the naive approach.Wir untersuchen verteilte Systeme, mit besonderem Augenmerk auf Graphenprobleme und Fehlertoleranz. Fehlertoleranz auf einem System-on-Chip (SoC) kann durch eine fehlertolerante Puls- Weiterleitung verbessert werden. Das bestehende Puls-Weiterleitungs-System TRIX toleriert Fehler indem es ein verteiltes System ist das nur aus sehr einfachen Knoten besteht. Wir zeigen dass selbst im typischen, fehlerfreien Fall TRIX sich weitaus besser verhält als man naiverweise erwarten würde: Statistische Analysen unserer simulierten Experimente zeigen, dass der Verzögerungs-Unterschied eine Standardabweichung von lediglich O(log logH) erreicht, wobei H die Höhe des TRIX-Netzes ist. Das Generalisieren einiger klassischer Graphen-Probleme auf Distanz r kann uns neue Erkenntnisse bescheren über den Zusammenhang zwischen Distanz und Komplexität eines Problems. Für das Problem der dominierenden Mengen auf Distanz r zeigen wir sowohl eine algorithmische obere Schranke als auch eine bedingungsfreie untere Schranke für jede Klasse von Graphen, die bestimmte Eigenschaften an Umfang und Dichte erfüllt. Konkret erreicht unser Algorithmus in Zeit O(r) eine Annäherungsgüte von O(r · f(r)). Für konstante r bedeutet das, dass der Algorithmus in konstanter Zeit eine Annäherung konstanter Güte erreicht. Weiterhin zeigen wir, dass kein Algorithmus in Zeit O(r) eine Annäherungsgüte besser als 2r + 1 erreichen kann, nicht einmal in der Klasse der Kreis-Graphen von Umfang mindestens 5r. Weiterhin haben wir das Paketweiterleitungs-Problem untersucht, welches sich mit der Frage beschäftigt, wann genau Pakete in einem verteilten System idealerweise weitergeleitetwerden sollten. Die Paketewerden dabei von einem Gegenspieler eingefügt. Wir bauen auf dem existierenden Algorithmus OED auf, um mehr als ein Paket-Ziel beliefern zu können. Dadurch zeigen wir, dass Paket-Speicher der Größe O(log n) für dieses Problem ausreichen, im Gegensatz zu den Paket-Speichern der Größe O(n) die für einen naiven Ansatz nötig wären

Low-Concentrating, Stationary Solar Thermal Collectors for Process Heat Generation

The annual gain of stationary solar thermal collectors can be increased by non-focusing reflectors. Such concentrators make use of diffuse irradiance. A collector’s incidence angle modifier for diffuse (diffuse-IAM) accounts for this utilization. The diffuse irra-diance varies over the collector hemisphere, which dynamically influences the diffuse-IAM. This is not considered by state-of-the-art collector models. They simply calculate with one constant IAM value for isotropic diffuse irradiance from sky and ground. This work is based on the development of a stationary, double-covered process heat flat-plate collector with a one-sided, segmented booster reflector (RefleC). This reflector approximates one branch of a compound parabolic concentrator (CPC). Optical meas-urement results of the collector components as well as raytracing results of different variants are given. The thermal and optical characterization of test samples up to 190 °C in an outdoor laboratory as well as the validation of the raytracing are discussed. A collector simulation model with varying diffuse-IAM is described. Therein, ground reflected and sky diffuse irradiance are treated separately. Sky diffuse is weighted with an anisotropic IAM, which is re-calculated in every time step. This is realized by gener-ating an anisotropic sky radiance distribution with the model of Brunger and Hooper, and by weighting the irradiance from distinct sky elements with their raytraced beam-IAM values. According to the simulations, the RefleC booster increases the annual out-put of the double-covered flat-plate in Würzburg, Germany, by 87 % at a constant inlet temperature of 120 °C and by 20 % at 40 °C. Variations of the sky diffuse-IAM of up to 25 % during one day are found. A constant, isotropic diffuse-IAM would have under-valued the gains from the booster by 40 % at 40 °C and by 20 % at 120 °C. The results indicate that the gain of all non-focusing solar collectors is undervalued when constant, isotropic diffuse-IAMs calculated from raytracing or steady-state test data are used. Process heat generation with RefleC is demonstrated in a monitored pilot plant at work-ing temperatures of up to 130 °C. The measured annual system utilization ratio is 35 %. Comparing the gains at all inlet temperatures above 80 °C, the booster increases the an-nual output of the double-covered flat-plates by 78 %. Taking all inlet temperatures, the total annual gains of RefleC are 39 % above that of the flat-plates without reflectors. A qualitative comparison of the new simulation model results to the laboratory results and monitoring data shows good agreement. It is shown that the accuracy of existing collector models can be increased with low effort by calculating separate isotropic IAMs for diffuse sky and ground reflected irradiance. The highest relevance of this work is seen for stationary collectors with very distinctive radiation acceptance

Proceedings of the NASA Conference on Space Telerobotics, volume 4

Papers presented at the NASA Conference on Space Telerobotics are compiled. The theme of the conference was man-machine collaboration in space. The conference provided a forum for researchers and engineers to exchange ideas on the research and development required for the application of telerobotic technology to the space systems planned for the 1990's and beyond. Volume 4 contains papers related to the following subject areas: manipulator control; telemanipulation; flight experiments (systems and simulators); sensor-based planning; robot kinematics, dynamics, and control; robot task planning and assembly; and research activities at the NASA Langley Research Center

Multivariate characterisation of dual-layered catalysts, reliability and durability of Polymer Electrolyte Membrane Fuel Cells

Hydrogen fuel cells have held out the promise of clean, sustainable power generation for decades, but have failed to deliver on that potential. Inefficiencies in research and development work can be overcome to increase the rate of new knowledge acquisition in this field. A number of medical and engineering disciplines utilise a wide variety of statistical tools in their research to achieve this same end, but there has been little adoption of such statistical approaches within the fuel cell research community. This research undertakes a design of experiments (DoE) approach to the analysis of multiply-covarying (M-ANOVAR) factors by using historic data, and direct experimental work, on a wide variety of polymer electrolyte membrane fuel cells (PEMFCs) cathode gas diffusion media (GDM) and dual layered catalyst structures. This research developed a gradient of polarisation regions' approach; a method for making robust numerical comparisons between large numbers of samples based on polarisation curves, while still measuring the more usual peak power of the PEMFC. The assessment of polarisation gradients was completed in a statistically robust fashion that enabled the creation of regression models of GDMs for multiple input and multiple output data sets. Having established the multivariate method; a set of possibly co-varying factors, a DoE approach was used to assess GDM selection, dual layered catalyst structures and degradation of membrane electrode assembly (MEA) performance over time. Degradation studies monopolise resources to be monopolised for protracted periods. M-ANOVAR allows the addition of other factors in the study, and the total efficiency of the degradation experiment is increased. A 20% reduction in the number of samples to be tested was achieved in the case study presented in this thesis (compared to the usual one factor at a time (OFAT) approach). This research highlights the flexibility and efficiency of DoE approaches to PEMFC degradation experimentation. This research is unique in that it creates catalyst ink formulations where the variation in catalyst loading in each sub-layer of the catalyst layer (CL) was achieved by having a different concentration of the catalyst material on the carbon supports. The final M-ANOVAR analysis indicates a simple average of the individual responses was appropriate for the experiments undertaken. It was shown that low concentration dual layer catalysts on paper GDMs have improved performance compared to paper GDMs with uniform, single layer catalysts: Demonstrating reduced platinum concentrations to achieve equivalent open cell performance. The time to peak power during testing (how long after starting the test it takes to achieve the maximum performance in the cell) was strongly impacted by GDM selection. Furthermore, there was a strong suggestion that previously published results crediting a change in performance due to a single layer, or multi-layered catalyst structures may, in fact, have been due to the selection of GDM used in the experiment instead

Space Power

Appropriate directions for the applied research and technology programs that will develop space power systems for U.S. future space missions beyond 1995 are explored. Spacecraft power supplies; space stations, space power reactors, solar arrays, thermoelectric generators, energy storage, and communication satellites are among the topics discussed