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

Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee certain required consistency properties (e.g., connectivity of the topology), while achieving desired optimization properties (e.g., a bounded number of neighbors). Real-world topologies are dynamic (e.g., because nodes join, leave, or move within the network), which requires topology control algorithms to operate in an incremental way, i.e., based on the recently introduced modifications of a topology. Visual programming and specification languages are a proven means for specifying the structure as well as consistency and optimization properties of topologies. In this paper, we present a novel methodology, based on a visual graph transformation and graph constraint language, for developing incremental topology control algorithms that are guaranteed to fulfill a set of specified consistency and optimization constraints. More specifically, we model the possible modifications of a topology control algorithm and the environment using graph transformation rules, and we describe consistency and optimization properties using graph constraints. On this basis, we apply and extend a well-known constructive approach to derive refined graph transformation rules that preserve these graph constraints. We apply our methodology to re-engineer an established topology control algorithm, kTC, and evaluate it in a network simulation study to show the practical applicability of our approachComment: This document corresponds to the accepted manuscript of the referenced journal articl

Scalable partitioning for parallel position based dynamics

We introduce a practical partitioning technique designed for parallelizing Position Based Dynamics, and exploiting the ubiquitous multi-core processors present in current commodity GPUs. The input is a set of particles whose dynamics is influenced by spatial constraints. In the initialization phase, we build a graph in which each node corresponds to a constraint and two constraints are connected by an edge if they influence at least one common particle. We introduce a novel greedy algorithm for inserting additional constraints (phantoms) in the graph such that the resulting topology is q-colourable, where ˆ qˆ ≥ 2 is an arbitrary number. We color the graph, and the constraints with the same color are assigned to the same partition. Then, the set of constraints belonging to each partition is solved in parallel during the animation phase. We demonstrate this by using our partitioning technique; the performance hit caused by the GPU kernel calls is significantly decreased, leaving unaffected the visual quality, robustness and speed of serial position based dynamics

Semantic validation of affinity constrained service function chain requests

Network Function Virtualization (NFV) has been proposed as a paradigm to increase the cost-efficiency, flexibility and innovation in network service provisioning. By leveraging IT virtualization techniques in combination with programmable networks, NFV is able to decouple network functionality from the physical devices on which they are deployed. This opens up new business opportunities for both Infrastructure Providers (InPs) as well as Service Providers (SPs), where the SP can request to deploy a chain of Virtual Network Functions (VNFs) on top of which its service can run. However, current NFV approaches lack the possibility for SPs to define location requirements and constraints on the mapping of virtual functions and paths onto physical hosts and links. Nevertheless, many scenarios can be envisioned in which the SP would like to attach placement constraints for efficiency, resilience, legislative, privacy and economic reasons. Therefore, we propose a set of affinity and anti-affinity constraints, which can be used by SPs to define such placement restrictions. This newfound ability to add constraints to Service Function Chain (SFC) requests also introduces an additional risk that SFCs with conflicting constraints are requested or automatically generated. Therefore, a framework is proposed that allows the InP to check the validity of a set of constraints and provide feedback to the SP. To achieve this, the SFC request and relevant information on the physical topology are modeled as an ontology of which the consistency can be checked using a semantic reasoner. Enabling semantic validation of SFC requests, eliminates inconsistent SFCs requests from being transferred to the embedding algorithm.Peer Reviewe

Unconstraining Graph-Constrained Group Testing

In network tomography, one goal is to identify a small set of failed links in a network using as little information as possible. One way of setting up this problem is called graph-constrained group testing. Graph-constrained group testing is a variant of the classical combinatorial group testing problem, where the tests that one is allowed are additionally constrained by a graph. In this case, the graph is given by the underlying network topology. The main contribution of this work is to show that for most graphs, the constraints imposed by the graph are no constraint at all. That is, the number of tests required to identify the failed links in graph-constrained group testing is near-optimal even for the corresponding group testing problem with no graph constraints. Our approach is based on a simple randomized construction of tests. To analyze our construction, we prove new results about the size of giant components in randomly sparsified graphs. Finally, we provide empirical results which suggest that our connected-subgraph tests perform better not just in theory but also in practice, and in particular perform better on a real-world network topology

Constraining 3D Magnetic Field Extrapolations Using The Twin Perspectives of STEREO

The 3D magnetic topology of a solar active region (NOAA 10956) was reconstructed using a linear force-free field extrapolation constrained using the twin perspectives of \emph{STEREO}. A set of coronal field configurations was initially generated from extrapolations of the photospheric magnetic field observed by the Michelson Doppler Imager (MDI) on \emph{SOHO}. Using an EUV intensity-based cost function, the extrapolated field lines that were most consistent with 171\AA\ passband images from the Extreme UltraViolet Imager (EUVI) on \emph{STEREO} were identified. This facilitated quantitative constraints to be placed on the twist ($\alpha$) of the extrapolated field lines, where $\nabla \times {\bf B} = \alpha {\bf B}$. Using the constrained values of $\alpha$, the evolution in time of twist, connectivity, and magnetic energy were then studied. A flux emergence event was found to result in significant changes in the magnetic topology and total magnetic energy of the region