Network and Index Coding with Application to Robust and Secure Communications

Since its introduction in the year 2000 by Ahlswede et al., the network coding paradigm has revolutionized the way we understand information flows in networks. Traditionally, information transmitted in a communication network was treated as a commodity in a transportation network, much like cars on highways or fluids in pipes. This approach, however, fails to capture the very nature of information, which in contrast to material goods, can be coded and decoded. The network coding techniques take full advantage of the inherent properties of information, and allow the nodes in a network, not only to store and forward, but also to "mix", i.e., encode, their received data. This approach was shown to result in a substantial throughput gain over the traditional routing and tree packing techniques. In this dissertation, we study applications of network coding for guarantying reliable and secure information transmission in networks with compromised edges. First, we investigate the construction of robust network codes for achieving network resilience against link failures. We focus on the practical important case of unicast networks with non-uniform edge capacities where a single link can fail at a time. We demonstrate that these networks exhibit unique structural properties when they are minimal, i.e., when they do not contain redundant edges. Based on this structure, we prove that robust linear network codes exist for these networks over GF(2), and devise an efficient algorithm to construct them. Second, we consider the problem of securing a multicast network against an eavesdropper that can intercept the packets on a limited number of network links. We recast this problem as a network generalization of the classical wiretap channel of Type II introduced by Ozarow and Wyner in 1984. In particular, we demonstrate that perfect secrecy can be achieved by using the Ozarow-Wyner scheme of coset coding at the source, on top of the implemented network code. Consequently, we transparently recover important results available in the literature on secure network coding. We also derive new bounds on the required secure code alphabet size and an algorithm for code construction. In the last part of this dissertation, we study the connection between index coding, network coding, and matroid linear representation. We devise a reduction from the index coding problem to the network coding problem, implying that in the linear case these two problems are equivalent. We also present a second reduction from the matroid linear representability problem to index coding, and therefore, to network coding. The latter reduction establishes a strong connection between matroid theory and network coding theory. These two reductions are then used to construct special instances of the index coding problem where vector linear codes outperform scalar linear ones, and where non-linear encoding is needed to achieve the optimal number of transmission. Thereby, we provide a counterexample to a related conjecture in the literature and demonstrate the benefits of vector linear codes

Importance Sampling-Based Monte Carlo Methods with Applications to Quantitative Finance

In the present work advanced Monte Carlo methods for discrete-time stochastic processes are developed and investigated. A particular focus is on sequential Monte Carlo methods (particle filters and particle smoothers) which allow the estimation of nonlinear, non-Gaussian state-space models. The key technique which underlies the proposed algorithms is importance sampling. Computationally efficient nonparametric variants of importance sampling which are generally applicable are developed. Asymptotic properties of these methods are analyzed theoretically and it is shown empirically that they improve over existing methods for relevant applications. Particularly, it is shown that they can be applied for financial derivative pricing which constitutes a high-dimensional integration problem and that they can be used to improve sequential Monte Carlo methods. Original models in general state-space form for two important applications are proposed and new sequential Monte Carlo algorithms for their estimation are developed. The first application concerns the on-line estimation of the spot cross-volatility for ultra high-frequency financial data. This is a challenging problem because of the presence of microstructure noise and nonsynchronous trading. For the first time state-space models with non-synchronously evolving states and observations are discussed and a particle filter which can cope with these models is designed. In addition, a new sequential variant of the EM algorithm for parameter estimation is proposed. The second application is a non-linear model for time series with an oscillatory pattern and a phase process in the background. This model can be applied, for instance, to noisy quasiperiodic oscillators occurring in physics and other fields. The estimation of the model is based on an advanced particle smoother and a new nonparametric EM algorithm. The dissertation is accompanied by object-oriented C++ implementations of all proposed algorithms which were developed with a focus on reusability and extendability

Framework for privacy-aware content distribution in peer-to- peer networks with copyright protection

The use of peer-to-peer (P2P) networks for multimedia distribution has spread out globally in recent years. This mass popularity is primarily driven by the efficient distribution of content, also giving rise to piracy and copyright infringement as well as privacy concerns. An end user (buyer) of a P2P content distribution system does not want to reveal his/her identity during a transaction with a content owner (merchant), whereas the merchant does not want the buyer to further redistribute the content illegally. Therefore, there is a strong need for content distribution mechanisms over P2P networks that do not pose security and privacy threats to copyright holders and end users, respectively. However, the current systems being developed to provide copyright and privacy protection to merchants and end users employ cryptographic mechanisms, which incur high computational and communication costs, making these systems impractical for the distribution of big files, such as music albums or movies.El uso de soluciones de igual a igual (peer-to-peer, P2P) para la distribución multimedia se ha extendido mundialmente en los últimos años. La amplia popularidad de este paradigma se debe, principalmente, a la distribución eficiente de los contenidos, pero también da lugar a la piratería, a la violación del copyright y a problemas de privacidad. Un usuario final (comprador) de un sistema de distribución de contenidos P2P no quiere revelar su identidad durante una transacción con un propietario de contenidos (comerciante), mientras que el comerciante no quiere que el comprador pueda redistribuir ilegalmente el contenido más adelante. Por lo tanto, existe una fuerte necesidad de mecanismos de distribución de contenidos por medio de redes P2P que no supongan un riesgo de seguridad y privacidad a los titulares de derechos y los usuarios finales, respectivamente. Sin embargo, los sistemas actuales que se desarrollan con el propósito de proteger el copyright y la privacidad de los comerciantes y los usuarios finales emplean mecanismos de cifrado que implican unas cargas computacionales y de comunicaciones muy elevadas que convierten a estos sistemas en poco prácticos para distribuir archivos de gran tamaño, tales como álbumes de música o películas.L'ús de solucions d'igual a igual (peer-to-peer, P2P) per a la distribució multimèdia s'ha estès mundialment els darrers anys. L'àmplia popularitat d'aquest paradigma es deu, principalment, a la distribució eficient dels continguts, però també dóna lloc a la pirateria, a la violació del copyright i a problemes de privadesa. Un usuari final (comprador) d'un sistema de distribució de continguts P2P no vol revelar la seva identitat durant una transacció amb un propietari de continguts (comerciant), mentre que el comerciant no vol que el comprador pugui redistribuir il·legalment el contingut més endavant. Per tant, hi ha una gran necessitat de mecanismes de distribució de continguts per mitjà de xarxes P2P que no comportin un risc de seguretat i privadesa als titulars de drets i els usuaris finals, respectivament. Tanmateix, els sistemes actuals que es desenvolupen amb el propòsit de protegir el copyright i la privadesa dels comerciants i els usuaris finals fan servir mecanismes d'encriptació que impliquen unes càrregues computacionals i de comunicacions molt elevades que fan aquests sistemes poc pràctics per a distribuir arxius de grans dimensions, com ara àlbums de música o pel·lícules

Interval and Possibilistic Methods for Constraint-Based Metabolic Models

This thesis is devoted to the study and application of constraint-based metabolic models. The objective was to find simple ways to handle the difficulties that arise in practice due to uncertainty (knowledge is incomplete, there is a lack of measurable variables, and those available are imprecise). With this purpose, tools have been developed to model, analyse, estimate and predict the metabolic behaviour of cells. The document is structured in three parts. First, related literature is revised and summarised. This results in a unified perspective of several methodologies that use constraint-based representations of the cell metabolism. Three outstanding methods are discussed in detail, network-based pathways analysis (NPA), metabolic flux analysis (MFA), and flux balance analysis (FBA). Four types of metabolic pathways are also compared to clarify the subtle differences among them. The second part is devoted to interval methods for constraint-based models. The first contribution is an interval approach to traditional MFA, particularly useful to estimate the metabolic fluxes under data scarcity (FS-MFA). These estimates provide insight on the internal state of cells, which determines the behaviour they exhibit at given conditions. The second contribution is a procedure for monitoring the metabolic fluxes during a cultivation process that uses FS-MFA to handle uncertainty. The third part of the document addresses the use of possibility theory. The main contribution is a possibilistic framework to (a) evaluate model and measurements consistency, and (b) perform flux estimations (Poss-MFA). It combines flexibility on the assumptions and computational efficiency. Poss-MFA is also applied to monitoring fluxes and metabolite concentrations during a cultivation, information of great use for fault-detection and control of industrial processes. Afterwards, the FBA problem is addressed.Llaneras Estrada, F. (2011). Interval and Possibilistic Methods for Constraint-Based Metabolic Models [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10528Palanci

Meta-Heuristics for the Multiple Trip Vehicle Routing Problem with Backhauls

With the growing and more accessible computational power, the demand for robust and sophisticated computerised optimisation is increasing for logistical problems. By making good use of computational technologies, the research in this thesis concentrates on efficient fleet management by studying a class of vehicle routing problems and developing efficient solution algorithms. The literature review in this thesis looks at VRPs from various development angles. The search reveals that from the problem modelling side clear efforts are made to bring the classical VRP models closer to reality by developing various variants. However, apart from the real VRP applications (termed as 'rich' VRPs), it is also noticeable that these classical VRP based variants address merely one or two additional characteristics from the real routing problem issues, concentrating on either operational (fleet management) or tactical (fleet acquisition) aspects. This thesis certainly hopes to add to one of those good efforts which have helped in bringing the VRPs closer to reality through addressing both the operational as well as the tactical aspects. On the solution methodologies development side, the proposed research noted some considerable and impressive developments. Although, it is well established that the VRPs belong to the NP-hard combinatorial class of problems, there are considerable efforts on the development of exact methods. However the literature is full of a variety of heuristic methodologies including the classical and the most modern hybrid approaches. Among the hybrid approaches, the most recent one noted is mat-heuristics that combine heuristics and mathematical programming techniques to solve combinatorial optimisation problems. The mat-heuristics approaches appear to be comparatively in its infant age at this point in time. However this is an exciting area of research which seeks more attention in the literature. Hence, a good part of this research is devoted to the development of a hybrid approach that combines heuristics and mathematical programming techniques. When reviewing the specific literature on the VRP problems focused in this thesis, the vehicle routing problem with backhauls (VRPB) and the multiple trip vehicle routing problem (MT-VRP), there is not sufficient development on the problem modelling side in terms of bringing these two problems closer to the reality. Hence, to fill the gap this thesis introduces and investigates a new variant, the multiple trip vehicle routing problem with backhauls (MT-VRPB) that combines the above two variants of the VRP. The problem is first described thoroughly and a new ILP (Integer Linear Programming) mathematical formulation of the MT-VRPB along with its possible variations is presented. The MT-VRPB is then solved optimally by using CPLEX along with providing an illustrative example showing the validation of the mathematical formulation. As part of the contribution, a large set of MT-VRPB data instances is created which is made available for future benchmarking. The CPLEX implementation produced optimal solutions for a good number of small and medium size data instances of the MT-VRPB and generated lower bounds for all instances. The CPLEX success may be considered as modest, but the produced results proved very important for the validation of the heuristic results produced in the thesis. To solve the larger instances of the MT-VRPB, a two level VNS algorithm called 'Two-Level VNS' is developed. It was noticed from the literature that the choice of using VNS for the VRPs has increased in recent literature due to its simplicity and speed. However our initial experiments with the classical VNS indicated that the algorithm is more inclined towards the intensification side. Hence, the Two-Level VNS is designed to obtain a maximum balance of the diversification and the intensification during the search process. It is achieved by incorporating a sub-set of neighbourhood structures and a sus-set of local search refinement routines and hence, a full set of neighbourhood structures and a full set of local search refinement routines at two levels of the algorithm respectively. The algorithm found very encouraging results when compared with the solutions found by CPLEX. These findings in this thesis demonstrate the power of VNS yet again in terms of its speed, simplicity and efficiency. To investigate this new variant further, we developed an algorithm belonging to the new class of the hybrid methodologies, i.e., mat-heuristics. A hybrid collaborative sequential mat-heuristic approach called the CSMH to solve the MT-VRPB is developed. The exact method approach produced in Chapter 4 is then hybridised with the Two-Level VNS algorithm developed in Chapter 5. The overall performance of the CSMH remained very encouraging in terms of the solution quality and the time taken on average compared with the CPLEX and the Two-Level VNS meta-heuristic. To demonstrate the power and effectiveness of our methodologies, we tested the designed algorithms on the two special versions of the VRP (i.e., VRPB and MT-VRP) to assess whether they are efficient and dynamic enough to solve a range of VRP variants. Hence the Two-Level VNS and the CSMH algorithms developed to solve the MT-VRPB are adapted accordingly and implemented to solve the two above variants separately. The algorithms produced very competitive results for the benchmark data sets when compared to the best known solutions from the literature. The successful implementations of these algorithms on the three VRP models with only minor amendments prove their generalizability and their robustness. The results in this research show that significant cost savings could be obtained by choosing the right fleet size and better vehicle utilisations with multiple trips and backhauling. Hence, the research proved the justification of studying this interesting combination. Moreover, the problem modelling, efficient algorithm design and implementation, and the research results reveal some vital information and implications from the managerial point of view in terms of making the tactical (fleet acquisition) and the operational (fleet management) decisions in a more informative manner