Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;

The Quantum Hall Effect of Field Induced Spin Density Wave Phases: the Physics of the Ultra Quantum Crystal

The Quantum Hall Effect of Field Induced Spin Density Wave Phases is accounted for within a weak coupling theory which assumes that in the relevant low temperature part of the phase diagram the quasi one dimensional conductor is well described by Fermi liquid theory. Recent experimental results show that sign inversion of the Hall Plateaux takes place all the way down from the instability line of the normal state. The Quantum Nesting model, when it takes into account small perturbations away from perfect nesting, describes well not only the usual sequence of Hall plateaux, but also the anomalies connected with sign inversion of the Hall Effect. Experimental observation of de-doubling of sub-phase to sub-phase transition lines suggests that superposition of SDW order parameters occurs in some parts of the phase diagram. The collective excitations of the Ultra Quantum Crystal have a specific magneto-roton structure. The SDW case exhibits,apart from the usual spin waves, topological excitations which are either skyrmions or half skyrmions. It is suggested that magneto-rotons may have been observed some years ago in specific heat experiments.Comment: 17 pages, latex, 6 figures, available on request at [email protected]

A contribution to the evaluation and optimization of networks reliability

L’évaluation de la fiabilité des réseaux est un problème combinatoire très complexe qui nécessite des moyens de calcul très puissants. Plusieurs méthodes ont été proposées dans la littérature pour apporter des solutions. Certaines ont été programmées dont notamment les méthodes d’énumération des ensembles minimaux et la factorisation, et d’autres sont restées à l’état de simples théories. Cette thèse traite le cas de l’évaluation et l’optimisation de la fiabilité des réseaux. Plusieurs problèmes ont été abordés dont notamment la mise au point d’une méthodologie pour la modélisation des réseaux en vue de l’évaluation de leur fiabilités. Cette méthodologie a été validée dans le cadre d’un réseau de radio communication étendu implanté récemment pour couvrir les besoins de toute la province québécoise. Plusieurs algorithmes ont aussi été établis pour générer les chemins et les coupes minimales pour un réseau donné. La génération des chemins et des coupes constitue une contribution importante dans le processus d’évaluation et d’optimisation de la fiabilité. Ces algorithmes ont permis de traiter de manière rapide et efficace plusieurs réseaux tests ainsi que le réseau de radio communication provincial. Ils ont été par la suite exploités pour évaluer la fiabilité grâce à une méthode basée sur les diagrammes de décision binaire. Plusieurs contributions théoriques ont aussi permis de mettre en place une solution exacte de la fiabilité des réseaux stochastiques imparfaits dans le cadre des méthodes de factorisation. A partir de cette recherche plusieurs outils ont été programmés pour évaluer et optimiser la fiabilité des réseaux. Les résultats obtenus montrent clairement un gain significatif en temps d’exécution et en espace de mémoire utilisé par rapport à beaucoup d’autres implémentations. Mots-clés: Fiabilité, réseaux, optimisation, diagrammes de décision binaire, ensembles des chemins et coupes minimales, algorithmes, indicateur de Birnbaum, systèmes de radio télécommunication, programmes.Efficient computation of systems reliability is required in many sensitive networks. Despite the increased efficiency of computers and the proliferation of algorithms, the problem of finding good and quickly solutions in the case of large systems remains open. Recently, efficient computation techniques have been recognized as significant advances to solve the problem during a reasonable period of time. However, they are applicable to a special category of networks and more efforts still necessary to generalize a unified method giving exact solution. Assessing the reliability of networks is a very complex combinatorial problem which requires powerful computing resources. Several methods have been proposed in the literature. Some have been implemented including minimal sets enumeration and factoring methods, and others remained as simple theories. This thesis treats the case of networks reliability evaluation and optimization. Several issues were discussed including the development of a methodology for modeling networks and evaluating their reliabilities. This methodology was validated as part of a radio communication network project. In this work, some algorithms have been developed to generate minimal paths and cuts for a given network. The generation of paths and cuts is an important contribution in the process of networks reliability and optimization. These algorithms have been subsequently used to assess reliability by a method based on binary decision diagrams. Several theoretical contributions have been proposed and helped to establish an exact solution of the stochastic networks reliability in which edges and nodes are subject to failure using factoring decomposition theorem. From this research activity, several tools have been implemented and results clearly show a significant gain in time execution and memory space used by comparison to many other implementations. Key-words: Reliability, Networks, optimization, binary decision diagrams, minimal paths set and cuts set, algorithms, Birnbaum performance index, Networks, radio-telecommunication systems, programs

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Information Theoretic Methods For Biometrics, Clustering, And Stemmatology

This thesis consists of four parts, three of which study issues related to theories and applications of biometric systems, and one which focuses on clustering. We establish an information theoretic framework and the fundamental trade-off between utility of biometric systems and security of biometric systems. The utility includes person identification and secret binding, while template protection, privacy, and secrecy leakage are security issues addressed. A general model of biometric systems is proposed, in which secret binding and the use of passwords are incorporated. The system model captures major biometric system designs including biometric cryptosystems, cancelable biometrics, secret binding and secret generating systems, and salt biometric systems. In addition to attacks at the database, information leakage from communication links between sensor modules and databases is considered. A general information theoretic rate outer bound is derived for characterizing and comparing the fundamental capacity, and security risks and benefits of different system designs. We establish connections between linear codes to biometric systems, so that one can directly use a vast literature of coding theories of various noise and source random processes to achieve good performance in biometric systems. We develop two biometrics based on laser Doppler vibrometry: LDV) signals and electrocardiogram: ECG) signals. For both cases, changes in statistics of biometric traits of the same individual is the major challenge which obstructs many methods from producing satisfactory results. We propose a ii robust feature selection method that specifically accounts for changes in statistics. The method yields the best results both in LDV and ECG biometrics in terms of equal error rates in authentication scenarios. Finally, we address a different kind of learning problem from data called clustering. Instead of having a set of training data with true labels known as in identification problems, we study the problem of grouping data points without labels given, and its application to computational stemmatology. Since the problem itself has no true answer, the problem is in general ill-posed unless some regularization or norm is set to define the quality of a partition. We propose the use of minimum description length: MDL) principle for graphical based clustering. In the MDL framework, each data partitioning is viewed as a description of the data points, and the description that minimizes the total amount of bits to describe the data points and the model itself is considered the best model. We show that in synthesized data the MDL clustering works well and fits natural intuition of how data should be clustered. Furthermore, we developed a computational stemmatology method based on MDL, which achieves the best performance level in a large dataset

Glosarium Matematika

273 p.; 24 cm