Hierarchical Up/Down Routing Architecture for Ethernet backbones and campus networks

We describe a new layer two distributed and scalable routing architecture. It uses an automatic hierarchical node identifier assignment mechanism associated to the rapid spanning tree protocol. Enhanced up/down mechanisms are used to prohibit some turns at nodes to break cycles, instead of blocking links like the spannning tree protocol does. The protocol performance is similar or better than other turn prohibition algorithms recently proposed with lower complexity O(Nd) and better scalability. Simulations show that the fraction of prohibited turns over random networks is less than 0.2. The effect of root bridge election on the performance of the protocol is limited both in the random and regular networks studied. The use of hierarchical, tree-descriptive addresses simplifies the routing, and avoids the need of all nodes having a global knowleddge of the network topology. Routing frames through the hierarchical tree at very high speed is possible by progressive decoding of frame destination address, without routing tables or port address learning. Coexistence with standard bridges is achieved using combined devices: bridges that forward the frames having global destination MAC addresses as standard bridges and frames with local MAC frames with the proposed protocol.Publicad

The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.Comment: 14 pages, 8 figure

HURP/HURBA: Zero-configuration hierarchical Up/Down routing and bridging architecture for Ethernet backbones and campus networks

Ethernet switched networks do not scale appropriately due to limitations inherent to the spanning tree protocol. Ethernet architectures based on routing over a virtual topology in which turns are prohibited offer improved performance over spanning tree, although in some cases suffer from excessive computational complexity. Up/Down routing is a turn prohibition algorithm with low computational complexity. In this paper we propose HURBA, a new layer-two architecture that improves Up/Down routing performance due to an optimization based on the use of hierarchical addressing, while preserving the computational complexity of Up/Down. The resulting architecture requires zero-configuration, uses the same frame format as Ethernet, allows upgrades by software update, and is compatible with 802.1D bridges by means of encapsulation. HURP protocol builds automatically a core with the interconnected HURP routing bridges and the standard bridges get connected to the edges in standard spanning trees. Simulations show that the performance of HURP, evaluated over various combinations of network topology and size, is close to the one of shortest path, is consistently better than that of Up/Down, and is equal or better than Turn Prohibition, with the advantage of having a lower complexity.En prens

Routing on the Channel Dependency Graph:: A New Approach to Deadlock-Free, Destination-Based, High-Performance Routing for Lossless Interconnection Networks

In the pursuit for ever-increasing compute power, and with Moore's law slowly coming to an end, high-performance computing started to scale-out to larger systems. Alongside the increasing system size, the interconnection network is growing to accommodate and connect tens of thousands of compute nodes. These networks have a large influence on total cost, application performance, energy consumption, and overall system efficiency of the supercomputer. Unfortunately, state-of-the-art routing algorithms, which define the packet paths through the network, do not utilize this important resource efficiently. Topology-aware routing algorithms become increasingly inapplicable, due to irregular topologies, which either are irregular by design, or most often a result of hardware failures. Exchanging faulty network components potentially requires whole system downtime further increasing the cost of the failure. This management approach becomes more and more impractical due to the scale of today's networks and the accompanying steady decrease of the mean time between failures. Alternative methods of operating and maintaining these high-performance interconnects, both in terms of hardware- and software-management, are necessary to mitigate negative effects experienced by scientific applications executed on the supercomputer. However, existing topology-agnostic routing algorithms either suffer from poor load balancing or are not bounded in the number of virtual channels needed to resolve deadlocks in the routing tables. Using the fail-in-place strategy, a well-established method for storage systems to repair only critical component failures, is a feasible solution for current and future HPC interconnects as well as other large-scale installations such as data center networks. Although, an appropriate combination of topology and routing algorithm is required to minimize the throughput degradation for the entire system. This thesis contributes a network simulation toolchain to facilitate the process of finding a suitable combination, either during system design or while it is in operation. On top of this foundation, a key contribution is a novel scheduling-aware routing, which reduces fault-induced throughput degradation while improving overall network utilization. The scheduling-aware routing performs frequent property preserving routing updates to optimize the path balancing for simultaneously running batch jobs. The increased deployment of lossless interconnection networks, in conjunction with fail-in-place modes of operation and topology-agnostic, scheduling-aware routing algorithms, necessitates new solutions to solve the routing-deadlock problem. Therefore, this thesis further advances the state-of-the-art by introducing a novel concept of routing on the channel dependency graph, which allows the design of an universally applicable destination-based routing capable of optimizing the path balancing without exceeding a given number of virtual channels, which are a common hardware limitation. This disruptive innovation enables implicit deadlock-avoidance during path calculation, instead of solving both problems separately as all previous solutions

IST Austria Thesis

This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph. For triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton. In the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars

Feature-sensitive and Adaptive Image Triangulation: A Super-pixel-based Scheme for Image Segmentation and Mesh Generation

With increasing utilization of various imaging techniques (such as CT, MRI and PET) in medical fields, it is often in great need to computationally extract the boundaries of objects of interest, a process commonly known as image segmentation. While numerous approaches have been proposed in literature on automatic/semi-automatic image segmentation, most of these approaches are based on image pixels. The number of pixels in an image can be huge, especially for 3D imaging volumes, which renders the pixel-based image segmentation process inevitably slow. On the other hand, 3D mesh generation from imaging data has become important not only for visualization and quantification but more critically for finite element based numerical simulation. Traditionally image-based mesh generation follows such a procedure as: (1) image boundary segmentation, (2) surface mesh generation from segmented boundaries, and (3) volumetric (e.g., tetrahedral) mesh generation from surface meshes. These three majors steps have been commonly treated as separate algorithms/steps and hence image information, once segmented, is not considered any more in mesh generation. In this thesis, we investigate a super-pixel based scheme that integrates both image segmentation and mesh generation into a single method, making mesh generation truly an image-incorporated approach. Our method, called image content-aware mesh generation, consists of several main steps. First, we generate a set of feature-sensitive, and adaptively distributed points from 2D grayscale images or 3D volumes. A novel image edge enhancement method via randomized shortest paths is introduced to be an optional choice to generate the features’ boundary map in mesh node generation step. Second, a Delaunay-triangulation generator (2D) or tetrahedral mesh generator (3D) is then utilized to generate a 2D triangulation or 3D tetrahedral mesh. The generated triangulation (or tetrahedralization) provides an adaptive partitioning of a given image (or volume). Each cluster of pixels within a triangle (or voxels within a tetrahedron) is called a super-pixel, which forms one of the nodes of a graph and adjacent super-pixels give an edge of the graph. A graph-cut method is then applied to the graph to define the boundary between two subsets of the graph, resulting in good boundary segmentations with high quality meshes. Thanks to the significantly reduced number of elements (super-pixels) as compared to that of pixels in an image, the super-pixel based segmentation method has tremendously improved the segmentation speed, making it feasible for real-time feature detection. In addition, the incorporation of image segmentation into mesh generation makes the generated mesh well adapted to image features, a desired property known as feature-preserving mesh generation

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions