Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems

A Systematic Approach to Constructing Families of Incremental Topology Control Algorithms Using Graph Transformation

In the communication systems domain, constructing and maintaining network topologies via topology control (TC) algorithms is an important cross-cutting research area. Network topologies are usually modeled using attributed graphs whose nodes and edges represent the network nodes and their interconnecting links. A key requirement of TC algorithms is to fulfill certain consistency and optimization properties to ensure a high quality of service. Still, few attempts have been made to constructively integrate these properties into the development process of TC algorithms. Furthermore, even though many TC algorithms share substantial parts (such as structural patterns or tie-breaking strategies), few works constructively leverage these commonalities and differences of TC algorithms systematically. In previous work, we addressed the constructive integration of consistency properties into the development process. We outlined a constructive, model-driven methodology for designing individual TC algorithms. Valid and high-quality topologies are characterized using declarative graph constraints; TC algorithms are specified using programmed graph transformation. We applied a well-known static analysis technique to refine a given TC algorithm in a way that the resulting algorithm preserves the specified graph constraints. In this paper, we extend our constructive methodology by generalizing it to support the specification of families of TC algorithms. To show the feasibility of our approach, we reneging six existing TC algorithms and develop e-kTC, a novel energy-efficient variant of the TC algorithm kTC. Finally, we evaluate a subset of the specified TC algorithms using a new tool integration of the graph transformation tool eMoflon and the Simonstrator network simulation framework.Comment: Corresponds to the accepted manuscrip

Convex Combinatorial Optimization

We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications

On the Optimality of Virtualized Security Function Placement in Multi-Tenant Data Centers

Security and service protection against cyber attacks remain among the primary challenges for virtualized, multi-tenant Data Centres (DCs), for reasons that vary from lack of resource isolation to the monolithic nature of legacy middleboxes. Although security is currently considered a property of the underlying infrastructure, diverse services require protection against different threats and at timescales which are on par with those of service deployment and elastic resource provisioning. We address the resource allocation problem of deploying customised security services over a virtualized, multi-tenant DC. We formulate the problem in Integral Linear Programming (ILP) as an instance of the NP-hard variable size variable cost bin packing problem with the objective of maximising the residual resources after allocation. We propose a modified version of the Best Fit Decreasing algorithm (BFD) to solve the problem in polynomial time and we show that BFD optimises the objective function up to 80% more than other algorithms

Exact two-terminal reliability of some directed networks

The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations, studies of the reliability polynomials, etc.) only provide approximations when the network's size increases, even when nodes do not fail and all edges have the same reliability p. We consider here a directed, generic graph of arbitrary size mimicking real-life long-haul communication networks, and give the exact, analytical solution for the two-terminal reliability. This solution involves a product of transfer matrices, in which individual reliabilities of edges and nodes are taken into account. The special case of identical edge and node reliabilities (p and rho, respectively) is addressed. We consider a case study based on a commonly-used configuration, and assess the influence of the edges being directed (or not) on various measures of network performance. While the two-terminal reliability, the failure frequency and the failure rate of the connection are quite similar, the locations of complex zeros of the two-terminal reliability polynomials exhibit strong differences, and various structure transitions at specific values of rho. The present work could be extended to provide a catalog of exactly solvable networks in terms of reliability, which could be useful as building blocks for new and improved bounds, as well as benchmarks, in the general case