131 research outputs found
On cycles and independence in graphs
Das erste Fachkapitel ist der Berechnung von Kreispackungszahlen, d.h. der maximalen Größe kanten- bzw. eckendisjunkter Kreispackungen, gewidmet. Da diese Probleme bekanntermaßen sogar für subkubische Graphen schwer sind, behandelt der erste Abschnitt die Komplexität des Packens von Kreisen einer festen Länge l in Graphen mit Maximalgrad Delta. Dieses für l=3 von Caprara und Rizzi gelöste Problem wird hier auf alle größeren Kreislängen l verallgemeinert. Der zweite Abschnitt beschreibt die Struktur von Graphen, für die die Kreispackungszahlen einen vorgegebenen Abstand zur zyklomatischen Zahl haben. Die 2-zusammenhängenden Graphen mit dieser Eigenschaft können jeweils durch Anwendung einer einfachen Erweiterungsregel auf eine endliche Menge von Graphen erzeugt werden. Aus diesem Strukturergebnis wird ein fpt-Algorithmus abgeleitet.
Das zweite Fachkapitel handelt von der Größenordnung der minimalen Anzahl von Kreislängen in einem Hamiltongraph mit q Sehnen. Eine Familie von Beispielen zeigt, dass diese Unterschranke höchstens die Wurzel von q+1 ist. Dem Hauptsatz dieses Kapitels zufolge ist die Zahl der Kreislängen eines beliebigen Hamiltongraphen mit q Sehnen mindestens die Wurzel von 4/7*q. Der Beweis beruht auf einem Lemma von Faudree et al., demzufolge der Graph, der aus einem Weg mit Endecken x und y und q gleichlangen Sehnen besteht, x-y-Wege von mindestens q/3 verschiedenen Längen enthält. Der erste Abschnitt enthält eine Korrektur des ursprünglich fehlerhaften Beweises und zusätzliche Schranken. Der zweite Abschnitt leitet daraus die Unterschranke für die Anzahl der Kreislängen ab.
Das letzte Fachkapitel behandelt Unterschranken für den Unabhängigkeitsquotienten, d.h. den Quotienten aus Unabhängigkeitszahl und Ordnung eines Graphen, für Graphen gegebener Dichte. In der Einleitung werden bestmögliche Schranken für die Klasse aller Graphen sowie für große zusammenhängende Graphen aus bekannten Ergebnissen abgeleitet. Danach wird die Untersuchung auf durch das Verbot kleiner ungerader Kreise eingeschränkte Graphenklassen ausgeweitet. Das Hauptergebnis des ersten Abschnitts ist eine Verallgemeinerung eines Ergebnisses von Heckman und Thomas, das die bestmögliche Schranke für zusammenhängende dreiecksfreie Graphen mit Durchschnittsgrad bis zu 10/3 impliziert und die extremalen Graphen charakterisiert. Der Rest der ersten beiden Abschnitte enthält Vermutungen ähnlichen Typs für zusammenhängende dreiecksfreie Graphen mit Durchschnittsgrad im Intervall [10/3, 54/13] und für zusammenhängende Graphen mit ungerader Taillenweite 7 mit Durchschnittsgrad bis zu 14/5. Der letzte Abschnitt enthält analoge Beobachtungen zum Bipartitionsquotienten. Die Arbeit schließt mit Vermutungen zu Unterschranken und die zugehörigen Klassen extremaler Graphen für den Bipartitionsquotienten.This thesis discusses several problems related to cycles and the independence number in graphs.
Chapter 2 contains problems on independent sets of cycles. It is known that it is hard to compute the maximum cardinality of edge-disjoint and vertex-disjoint cycle packings, even if restricted to subcubic graphs. Therefore, the first section discusses the complexity of a simpler problem: packing cycles of fixed length l in graphs of maximum degree Delta. The results of Caprara and Rizzi, who have solved this problem for l=3 are generalised to arbitrary lengths. The second section describes the structure of graphs for which the edge-disjoint resp. vertex-disjoint cycle packing number differs from the cyclomatic number by a constant. The corresponding classes of 2-connected graphs can be obtained by a simple extension rules applied to a finite set of graphs. This result implies a fixed-parameter-tractability result for the edge-disjoint and vertex-disjoint cycle packing numbers.
Chapter 3 contains an approximation of the minimum number of cycle lengths in a Hamiltonian graph with q chords. A family of examples shows that no more than the square root of q+1 can be guaranteed. The main result is that the square root of 4/7*q cycle lengths can be guaranteed. The proof relies on a lemma by Faudree et al.,
which states that the graph that contains a path with endvertices x and y and q chords of equal length contains paths between x and y of at least q/3 different lengths. The first section corrects the originally faulty proof and derives additional bounds. The second section uses these bounds to derive the lower bound on the size of the cycle spectrum.
Chapter 4 focuses on lower bounds on the independence ratio, i.e. the quotient of independence number and order of a graph, for graphs of given density. In the introduction, best-possible bounds both for arbitrary graphs and large connected graphs are derived from known results. Therefore, the rest of this chapter considers classes of graphs defined by forbidding small odd cycles as subgraphs. The main result of the first section is a generalisation of a result of Heckman and Thomas that determines the best possible lower bound for connected triangle-free graphs with average degree at most 10/3
and characterises the extremal graphs. The rest of the chapter is devoted to conjectures with similar statements on connected triangle-free graphs of average degree in [10/3, 54/13] and on connected graphs of odd girth 7 with average degree up to 14/5, similar conjectures for the bipartite ratio, possible classes of extremal graphs for these conjectures, and observations in support of the conjectures
Le jeu de policiers-voleur sur différentes classes de graphes
Réalisé avec le support financier du Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG) et du Fonds de Recherche du Québec – Nature et technologies (FRQNT).Ce mémoire étudie le jeu de policiers-voleur et contient trois articles, chacun portant sur une classe de graphes spécifique.
Dans le premier chapitre, la notation et les définitions de base de la théorie de graphe qui nous serons utiles sont introduites. Bien que chaque article comporte une introduction citant les concepts et résultats pertinents, le premier chapitre de ce mémoire contient aussi une introduction générale au jeu de policiers-voleur et présente certains des résultats majeurs sur ce jeu.
Le deuxième chapitre contient l’article écrit avec Seyyed Aliasghar Hosseini et Peter Bradshaw portant sur le jeu de policiers-voleurs sur les graphes de Cayley abéliens. Nous améliorons la borne supérieure sur le cop number de ces graphes en raffinant les méthodes utilisées précédemment par Hamidoune, Frankl et Bradshaw.
Le troisième chapitre présente l’article concernant le cop number des graphes 2K2-libres. Plus précisément, il est prouvé que 2 policiers peuvent toujours capturer le voleur sur ces graphes, prouvant ainsi la conjecture de Sivaraman et Testa.
Finalement, le quatrième chapitre est l’article écrit avec Samuel Yvon et porte sur les graphes qui ont cop number 4. Nous montrons que tous ces graphes ont au moins 19 sommets. En d’autres mots, 3 policiers peuvent toujours capturer le voleur sur tout graphe avec au plus 18 sommets, ce qui répond par la négative à une question de Andreae formulée en 1986. Un pan important de la preuve est faite par ordinateur; ce mémoire contient donc une annexe comprenant le code utilisé.This thesis studies the game of cops and robbers and consists of three articles, each considering a specific class of graphs.
In the first chapter, notation and basic definitions of graph theory are introduced. Al- though each article has an introduction citing the relevant concepts and results, the first chapter of this thesis also contains a general introduction to the game of cops and robbers and presents some of its major results.
The second chapter contains the paper written with Seyyed Aliasghar Hosseini and Peter Bradshaw on the game of cops and robbers on abelian Cayley graphs. We improve the upper bound on the cop number of these graphs by refining the methods used previously by Hamidoune, Frankl and Bradshaw.
The third chapter presents the paper concerning the cop number of 2K2-free graphs. More precisely, it is proved that 2 cops can always catch the robber on these graphs, proving a conjecture of Sivaraman and Testa.
Finally, the fourth chapter is the paper written with Samuel Yvon which deals with graphs of cop number 4. We show that such graphs have at least 19 vertices. In other words, 3 cops can always catch the robber on any graph with at most 18 vertices, which answers in the negative a question by Andreae from 1986. An important part of the proof is by computer; this thesis thus has an appendix containing the code used
Virtuaalse proovikabiini 3D kehakujude ja roboti juhtimisalgoritmide uurimine
Väitekirja elektrooniline versioon ei sisalda publikatsiooneVirtuaalne riiete proovimine on üks põhilistest teenustest, mille pakkumine võib suurendada rõivapoodide edukust, sest tänu sellele lahendusele väheneb füüsilise töö vajadus proovimise faasis ning riiete proovimine muutub kasutaja jaoks mugavamaks. Samas pole enamikel varem välja pakutud masinnägemise ja graafika meetoditel õnnestunud inimkeha realistlik modelleerimine, eriti terve keha 3D modelleerimine, mis vajab suurt kogust andmeid ja palju arvutuslikku ressurssi. Varasemad katsed on ebaõnnestunud põhiliselt seetõttu, et ei ole suudetud korralikult arvesse võtta samaaegseid muutusi keha pinnal. Lisaks pole varasemad meetodid enamasti suutnud kujutiste liikumisi realistlikult reaalajas visualiseerida. Käesolev projekt kavatseb kõrvaldada eelmainitud puudused nii, et rahuldada virtuaalse proovikabiini vajadusi. Välja pakutud meetod seisneb nii kasutaja keha kui ka riiete skaneerimises, analüüsimises, modelleerimises, mõõtmete arvutamises, orientiiride paigutamises, mannekeenidelt võetud 3D visuaalsete andmete segmenteerimises ning riiete mudeli paigutamises ja visualiseerimises kasutaja kehal. Selle projekti käigus koguti visuaalseid andmeid kasutades 3D laserskannerit ja Kinecti optilist kaamerat ning koostati nendest andmebaas. Neid andmeid kasutati välja töötatud algoritmide testimiseks, mis peamiselt tegelevad riiete realistliku visuaalse kujutamisega inimkehal ja suuruse pakkumise süsteemi täiendamisega virtuaalse proovikabiini kontekstis.Virtual fitting constitutes a fundamental element of the developments expected to rise the commercial prosperity of online garment retailers to a new level, as it is expected to reduce the load of the manual labor and physical efforts required. Nevertheless, most of the previously proposed computer vision and graphics methods have failed to accurately and realistically model the human body, especially, when it comes to the 3D modeling of the whole human body. The failure is largely related to the huge data and calculations required, which in reality is caused mainly by inability to properly account for the simultaneous variations in the body surface. In addition, most of the foregoing techniques cannot render realistic movement representations in real-time. This project intends to overcome the aforementioned shortcomings so as to satisfy the requirements of a virtual fitting room. The proposed methodology consists in scanning and performing some specific analyses of both the user's body and the prospective garment to be virtually fitted, modeling, extracting measurements and assigning reference points on them, and segmenting the 3D visual data imported from the mannequins. Finally, superimposing, adopting and depicting the resulting garment model on the user's body. The project is intended to gather sufficient amounts of visual data using a 3D laser scanner and the Kinect optical camera, to manage it in form of a usable database, in order to experimentally implement the algorithms devised. The latter will provide a realistic visual representation of the garment on the body, and enhance the size-advisor system in the context of the virtual fitting room under study
Investigation of ductile crack growth and normalization method for SE(T) specimen using finite element analyses
The fracture toughness resistance curve (e.g. J-R curve) is widely used in integrity assessment and strain-based design of oil and gas pipelines with respect to planar defects (i.e. cracks). This thesis includes two-dimensional (2D) and three-dimensional (3D) finite element analyses (FEA) of ductile crack growth of X80-grade pipeline steel based on the Gurson-Tvergaard-Needleman (GTN) constitutive model, and investigation of the normalization (NM) method to generate the J-R curve for the single-edge tension (SE(T)) specimen.
First, the GTN model implemented in the computational cell is adopted in the commercial software ABAQUS to calibrate the micromechanical parameters for the pipeline steel. Subsequently, the stable fracture process of six SE(T) and four single-edge bend (SE(B)) specimens tested are simulated in 3D and 2D FEA. Results have shown that the GTN model is a viable tool to predict the fracture behavior of the specimens, in terms of predicting the load-displacement curve, J-R curve and crack front profile of the fracture specimen. In addition, the stress field near the crack-tip as well as various constraint parameters are examined.
Second, based on the calibrated micromechanical parameters, a series of SE(T) specimens with various geometric configurations are modelled. The applicability of the NM method to generate J-R curves for SE(T) specimens is investigated, followed by the proposal of the so-called ‘k factor-based NM method’ based on the J-CMOD relationship, to improve the computational efficiency of the conventional NM method.
The outcomes of this study will facilitate and improve the evaluation of J-R curves for the SE(T) specimen using the NM method
Welding of X100 linepipe
The benefits of high strength steels in terms of reduced material volume due to
enhanced mechanical performance have been known for some time. Large diameter
transmission linepipe steels of minimum 690MPa ('XIOO') yield strength have been
developed throughout the previous decade, and have recently become commercially
available. Before these steels are used in linepipe construction projects, fimdamental
work regarding their ability to be field welded required undertaking. This thesis presents
data arising from girth welding experiments involving a variety of X 100 linepipe steels,
welding consurnables and welding processes.
Target girth weld mechanical properties thought suitable for a strain-based MOO
pipeline design were proposed at the outset of the research. Optimisation of pulsed gas
metal arc welding waveforms for the single and tandem wire processes, alongside the
establishment of the base material properties formed an early part of the research. An
extensive programme of solid wire welding consumable evaluation was then undertaken
for single, tandem and dual torch narrow gap welding processes. The majority of
equipment and procedures used throughout the work were as close to current field
practice as possible, to minimise the time required to transfer the technology to the field
situation. Work then focussed on the optimised alloy levels and welding procedure
requirements for the production of full girth welds, using a variety of industry pipeline
welding standards and supplemental techniques to assess the joint integrity.
It has been demonstrated that, subject to careful selection of welding consumable and
fairly precise control of welding process variables and parameters, there are no major
problems in obtaining weld metal strength levels of at least 120 MPa above the 690
MPa specified minimum yield strength (SMYS) of the parent pipe. This objective has
been achieved in welds made usirig all three mechanised process variants examined.
The desired target properties of strength and toughness were achieved with a variety of
consumables and pipe materials of different composition.
Tie-in and repair procedures were also developed during the course of the research, with
particular attention focussed on the application of high strength rutile flux cored ýVires.
These wires attained strength levels overmatching the pipe specified minimum yield
strength (690MPa), but would not reach the guaranteed overmatch level of 81 OMPa.
An examination of the thermocycles associated with four mechanised narrow gap
welding techniques (single, tandem, dual and dual tandem) was undertaken. The
experimental technique developed allowed the solidifying weld bead to be monitored, as
well as the cumulative temperature cycles experienced by the underlying layers.
Succesful determination of the cooling rates, times and transformation temperatures
allowed a comparative evaluation of the four processes, using an optimum weld metal
composition suitable for single wire welding of X100. This led to an understanding of
the metallurgical history, and its consequent effect on the associated mechanical and
microstructural properties. A similar series of experiments was undertaken to examine
these effects using variations in preheat with a single wire process. In most cases
considerable property variations were attained for'the same weld metal chemistry, joint
geometry and arc energy, highlighting the sensitivity of the process and procedure in
achieving the required properties. The high cooling rates determined from the thermocycle experiments explained the
microstructural and mechanical properties attainable from lean alloying levels. A series
of metal cored wires, based around the same alloy as for the thermocycle experiments,
was consequently manufactured to examine small changes in weld metal chemistry. The
individual wires involved changes in carbon, nickel, molybdenum and chromium to
examine potential property variations arising from a highly controlled narrow gap
welding procedure. The results again highlighted the sensitivity of the narrow gap
welding technique in generating considerable property variation within the weld metal.
Tolerance ranges for specific alloying additions to attain the proposed strength levels
with a single and tandem wire process were derived from the data
The computational complexity of approximation of partition functions
This thesis studies the computational complexity of approximately evaluating partition functions. For various classes of partition functions, we investigate whether there is an FPRAS: a fully polynomial randomised approximation scheme. In many of these settings we also study “expressibility”, a simple notion of defining a constraint by combining other constraints, and we show that the results cannot be extended by expressibility reductions alone. The main contributions are: -� We show that there is no FPRAS for evaluating the partition function of the hard-core gas model on planar graphs at fugacity 312, unless RP = NP. -� We generalise an argument of Jerrum and Sinclair to give FPRASes for a large class of degree-two Boolean #CSPs. -� We initiate the classification of degree-two Boolean #CSPs where the constraint language consists of a single arity 3 relation. -� We show that the complexity of approximately counting downsets in directed acyclic graphs is not affected by restricting to graphs of maximum degree three. -� We classify the complexity of degree-two #CSPs with Boolean relations and weights on variables. -� We classify the complexity of the problem #CSP(F) for arbitrary finite domains when enough non-negative-valued arity 1 functions are in the constraint language. -� We show that not all log-supermodular functions can be expressed by binary logsupermodular functions in the context of #CSPs
IST Austria Thesis
This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.
For triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.
In the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars
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Advanced experimental methods for the characterization of welded structures
Welding is one of the most prevalent techniques for mechanical fastening of metals. Recent developments in welding technology have led to welding techniques being more readily employed in safety-critical engineering structures. Since the existence of residual stresses and material property variation around welds affects the mechanical performance and thereby structural integrity, it is essential to improve our knowledge in understanding and modelling the mechanical response of the welded structures. The present work focuses on mechanical characterizations of such structures. This work can be broadly classified into two parts; the first part investigates the residual stress distribution in welded specimens of different metals and the second part presents investigations of mechanical properties in welded specimen using full field optical techniques.
A newly invented destructive technique for residual stress measurement, the contour method, was used for the investigations of the residual stress in welded joints in this study. The principle of the contour method is based on a variation of Bueckner's superposition theory. By means of a single straight cut, the 2D residual stress component normal to the region of interest can be determined. In this work, first the numerical simulations of the contour method using two and three dimensional bodies have been demonstrated. The contour method was then applied to one-pass and three-pass groove weld specimens and the results obtained from the contour method were compared to those obtained by the neutron diffraction strain measurement technique.
The capability of the contour method to measure multiple residual stress components was also investigated in this project. A recent development of the contour method of stress measurement, the multi-axial contour method, permits measurement of the 3D residual stress distribution in a body, based on the assumption that the residual stresses are due to an inelastic misfit strain (eigenstrain) that does not change when a sample containing residual stresses is sectioned. The eigenstrain is derived from measured displacements due to residual stress relaxation when the specimen is sectioned. By carrying out multiple cuts, the full residual stress tensor in a continuously processed body can then be determined. In this study, finite element simulations of the technique were carried out to verify the method numerically. The method was then used to determine the residual stresses in a VPP A-welded sample, and the results were validated by neutron diffraction measurements.
As part of the characterization of the welded structures, a study was undertaken to develop a method of extracting local mechanical properties from weld metal by strain mapping using the digital image correlation (DIC) technique. The feasibility of determining local stress-strain behaviour in the weld zone of a 316H stainless steel pipe with a girth weld was investigated by tensile tests on miniature and standard tensile test specimens. In addition, electron speckle pattern interferometry (ESPI) was utilized to obtain the full-field strain maps of a standard tensile specimen during loading and compared to those obtained in the same specimen by digital image correlation in order to verify the DIC measurements
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