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The increasing scale and complexity of computer networks imposes a need for highly flexible management mechanisms. The concept of network virtualization promises to provide this flexibility. Multiple arbitrary virtual networks can be constructed on top of a single substrate network. This allows network operators and service providers to tailor their network topologies to the specific needs of any offered service.
However, the assignment of resources proves to be a problem. Each newly defined virtual network must be realized by assigning appropriate physical resources. For a given set of virtual networks, two questions arise: Can all virtual networks be accommodated in the given substrate network? And how should the respective resources be assigned? The underlying problem is commonly known as the Virtual Network Embedding problem. A multitude of algorithms has already been proposed, aiming to provide solutions to that problem under various constraints. For the evaluation of these algorithms typically an empirical approach is adopted, using artificially created random problem instances. However, due to complex effects of random problem generation the obtained results can be hard to interpret correctly. A structured evaluation methodology that can avoid these effects is currently missing.
This thesis aims to fill that gap. Based on a thorough understanding of the problem itself, the effects of random problem generation are highlighted. A new simulation architecture is defined, increasing the flexibility for experimentation with embedding algorithms. A novel way of generating embedding problems is presented which migitates the effects of conventional problem generation approaches. An evaluation using these newly defined concepts demonstrates how new insights on algorithm behavior can be gained. The proposed concepts support experimenters in obtaining more precise and tangible evaluation data for embedding algorithms.
Since any encryption map may be viewed as a polynomial map between finite dimensional vector spaces over finite fields, the security of a cryptosystem can be examined by studying the difficulty of solving large systems of multivariate polynomial equations. Therefore, algebraic attacks lead to the task of solving polynomial systems over finite fields. In this thesis, we study several new algebraic techniques for polynomial system solving over finite fields, especially over the finite field with two elements. Instead of using traditional Gröbner basis techniques we focus on highly developed methods from several other areas like linear algebra, discrete optimization, numerical analysis and number theory. We study some techniques from combinatorial optimization to transform a polynomial system solving problem into a (sparse) linear algebra problem. We highlight two new kinds of hybrid techniques. The first kind combines the concept of transforming combinatorial infeasibility proofs to large systems of linear equations and the concept of mutants (finding special lower degree polynomials). The second kind uses the concept of mutants to optimize the Border Basis Algorithm. We study recent suggestions of transferring a system of polynomial equations over the finite field with two elements into a system of polynomial equalities and inequalities over the set of integers (respectively over the set of reals). In particular, we develop several techniques and strategies for converting the polynomial system of equations over the field with two elements to a polynomial system of equalities and inequalities over the reals (respectively over the set of integers). This enables us to make use of several algorithms in the field of discrete optimization and number theory. Furthermore, this also enables us to investigate the use of numerical analysis techniques such as the homotopy continuation methods and Newton's method. In each case several conversion techniques have been developed, optimized and implemented. Finally, the efficiency of the developed techniques and strategies is examined using standard cryptographic examples such as CTC and HFE. Our experimental results show that most of the techniques developed are highly competitive to state-of-the-art algebraic techniques.