Recursive Cube of Rings: A new topology for interconnection networks

In this paper, we introduce a family of scalable interconnection network topologies, named Recursive Cube of Rings (RCR), which are recursively constructed by adding ring edges to a cube. RCRs possess many desirable topological properties in building scalable parallel machines, such as fixed degree, small diameter, wide bisection width, symmetry, fault tolerance, etc. We first examine the topological properties of RCRs. We then present and analyze a general deadlock-free routing algorithm for RCRs. Using a complete binary tree embedded into an RCR with expansion-cost approximating to one, an efficient broadcast routing algorithm on RCRs is proposed. The upper bound of the number of message passing steps in one broadcast operation on a general RCR is also derived.published_or_final_versio

Communication aspects of parallel processing

Cover title.Includes bibliographical references.Supported in part by the Air Force Office of Scientific Research. AFOSR-88-0032Cüneyt Özveren

Embeddings Among Toruses and Meshes

Toruses and meshes include graphs of many varieties of topologies, with lines, rings, and hypercubes being special cases. Given a d-dimensional torus or mesh G and a c-dimensional torus or mesh H of the same size, we study the problem of embedding G in H to minimize the dilation cost. For increasing dimension cases (d \u3c c) in which the shapes of G and H satisfy the condition of expansion, the dilation costs of our embeddings are either 1 or 2, depending on the types of graphs of G and H. These embeddings a,re optimal except when G is a torus of even size and H is a mesh. For lowering dimension cases (d \u3e c) in which the shapes of G and H satisfy the condition of reduction, the dilation costs of our embeddings depend on the shapes of G and H. These embeddings, however, are not optimal in general. For the special cases in which G and H are square, the embedding results above can always be used to construct embeddings of G in H: these embeddings are all optimal for increasing dimension cases in which the dimension of H is divisible by the dimension of G, and all optimal to within a constant for fixed values of d and c for lowering dimension cases. Our main analysis technique is based on a generalization of Gray code for radix-2 (binary) numbering system to similar sequences for mixed-radix numbering systems

SCORPIO: A 36-Core Research Chip Demonstrating Snoopy Coherence on a Scalable Mesh NoC with In-Network Ordering

URL to conference programIn the many-core era, scalable coherence and on-chip interconnects are crucial for shared memory processors. While snoopy coherence is common in small multicore systems, directory-based coherence is the de facto choice for scalability to many cores, as snoopy relies on ordered interconnects which do not scale. However, directory-based coherence does not scale beyond tens of cores due to excessive directory area overhead or inaccurate sharer tracking. Prior techniques supporting ordering on arbitrary unordered networks are impractical for full multicore chip designs. We present SCORPIO, an ordered mesh Network-on-Chip(NoC) architecture with a separate fixed-latency, bufferless network to achieve distributed global ordering. Message delivery is decoupled from the ordering, allowing messages to arrive in any order and at any time, and still be correctly ordered. The architecture is designed to plug-and-play with existing multicore IP and with practicality, timing, area, and power as top concerns. Full-system 36 and 64-core simulations on SPLASH-2 and PARSEC benchmarks show an average application run time reduction of 24.1% and 12.9%, in comparison to distributed directory and AMD HyperTransport coherence protocols, respectively. The SCORPIO architecture is incorporated in an 11 mm-by- 13 mm chip prototype, fabricated in IBM 45nm SOI technology, comprising 36 Freescale e200 Power Architecture TM cores with private L1 and L2 caches interfacing with the NoC via ARM AMBA, along with two Cadence on-chip DDR2 controllers. The chip prototype achieves a post synthesis operating frequency of 1 GHz (833 MHz post-layout) with an estimated power of 28.8 W (768 mW per tile), while the network consumes only 10% of tile area and 19 % of tile power.United States. Defense Advanced Research Projects Agency (DARPA UHPC grant at MIT (Angstrom))Center for Future Architectures ResearchMicroelectronics Advanced Research Corporation (MARCO)Semiconductor Research Corporatio

A new-generation class of parallel architectures and their performance evaluation

The development of computers with hundreds or thousands of processors and capability for very high performance is absolutely essential for many computation problems, such as weather modeling, fluid dynamics, and aerodynamics. Several interconnection networks have been proposed for parallel computers. Nevertheless, the majority of them are plagued by rather poor topological properties that result in large memory latencies for DSM (Distributed Shared-Memory) computers. On the other hand, scalable networks with very good topological properties are often impossible to build because of their prohibitively high VLSI (e.g., wiring) complexity. Such a network is the generalized hypercube (GH). The GH supports full-connectivity of its nodes in each dimension and is characterized by outstanding topological properties. In addition, low-dimensional GHs have very large bisection widths. We propose in this dissertation a new class of processor interconnections, namely HOWs (Highly Overlapping Windows), that are more generic than the GH, are highly scalable, and have comparable performance. We analyze the communications capabilities of 2-D HOW systems and demonstrate that in practical cases HOW systems perform much better than binary hypercubes for important communications patterns. These properties are in addition to the good scalability and low hardware complexity of HOW systems. We present algorithms for one-to-one, one-to-all broadcasting, all-to-all broadcasting, one-to-all personalized, and all-to-all personalized communications on HOW systems. These algorithms are developed and evaluated for several communication models. In addition, we develop techniques for the efficient embedding of popular topologies, such as the ring, the torus, and the hypercube, into 1-D and 2-D HOW systems. The objective is to show that 2-D HOW systems are not only scalable and easy to implement, but they also result in good embedding of several classical topologies

Spectral methods for multimodal data analysis

Spectral methods have proven themselves as an important and versatile tool in a wide range of problems in the fields of computer graphics, machine learning, pattern recognition, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding a few of its eigenvalues and eigenfunctions. Classical examples include the computation of diffusion distances on manifolds in computer graphics, Laplacian eigenmaps, and spectral clustering in machine learning. In many cases, one has to deal with multiple data spaces simultaneously. For example, clustering multimedia data in machine learning applications involves various modalities or ``views'' (e.g., text and images), and finding correspondence between shapes in computer graphics problems is an operation performed between two or more modalities. In this thesis, we develop a generalization of spectral methods to deal with multiple data spaces and apply them to problems from the domains of computer graphics, machine learning, and image processing. Our main construction is based on simultaneous diagonalization of Laplacian operators. We present an efficient numerical technique for computing joint approximate eigenvectors of two or more Laplacians in challenging noisy scenarios, which also appears to be the first general non-smooth manifold optimization method. Finally, we use the relation between joint approximate diagonalizability and approximate commutativity of operators to define a structural similarity measure for images. We use this measure to perform structure-preserving color manipulations of a given image

New Fault Tolerant Multicast Routing Techniques to Enhance Distributed-Memory Systems Performance

Distributed-memory systems are a key to achieve high performance computing and the most favorable architectures used in advanced research problems. Mesh connected multicomputer are one of the most popular architectures that have been implemented in many distributed-memory systems. These systems must support communication operations efficiently to achieve good performance. The wormhole switching technique has been widely used in design of distributed-memory systems in which the packet is divided into small flits. Also, the multicast communication has been widely used in distributed-memory systems which is one source node sends the same message to several destination nodes. Fault tolerance refers to the ability of the system to operate correctly in the presence of faults. Development of fault tolerant multicast routing algorithms in 2D mesh networks is an important issue. This dissertation presents, new fault tolerant multicast routing algorithms for distributed-memory systems performance using wormhole routed 2D mesh. These algorithms are described for fault tolerant routing in 2D mesh networks, but it can also be extended to other topologies. These algorithms are a combination of a unicast-based multicast algorithm and tree-based multicast algorithms. These algorithms works effectively for the most commonly encountered faults in mesh networks, f-rings, f-chains and concave fault regions. It is shown that the proposed routing algorithms are effective even in the presence of a large number of fault regions and large size of fault region. These algorithms are proved to be deadlock-free. Also, the problem of fault regions overlap is solved. Four essential performance metrics in mesh networks will be considered and calculated; also these algorithms are a limited-global-information-based multicasting which is a compromise of local-information-based approach and global-information-based approach. Data mining is used to validate the results and to enlarge the sample. The proposed new multicast routing techniques are used to enhance the performance of distributed-memory systems. Simulation results are presented to demonstrate the efficiency of the proposed algorithms

Y-meshes and generalized pentagram maps

We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as $Y$-mutations in a cluster algebra and hence establish new connections between cluster theory and projective geometry. Our framework incorporates many preexisting generalized pentagram maps due to M. Gekhtman, M. Shapiro, S. Tabachnikov, and A. Vainshtein and also B. Khesin and F. Soloviev. In several of these cases a reduction to cluster dynamics was not previously known.Comment: 48 pages, 22 figures, to appear in Proceedings of the London Mathematical Societ

Similarity reasoning for local surface analysis and recognition

This thesis addresses the similarity assessment of digital shapes, contributing to the analysis of surface characteristics that are independent of the global shape but are crucial to identify a model as belonging to the same manufacture, the same origin/culture or the same typology (color, common decorations, common feature elements, compatible style elements, etc.). To face this problem, the interpretation of the local surface properties is crucial. We go beyond the retrieval of models or surface patches in a collection of models, facing the recognition of geometric patterns across digital models with different overall shape. To address this challenging problem, the use of both engineered and learning-based descriptions are investigated, building one of the first contributions towards the localization and identification of geometric patterns on digital surfaces. Finally, the recognition of patterns adds a further perspective in the exploration of (large) 3D data collections, especially in the cultural heritage domain. Our work contributes to the definition of methods able to locally characterize the geometric and colorimetric surface decorations. Moreover, we showcase our benchmarking activity carried out in recent years on the identification of geometric features and the retrieval of digital models completely characterized by geometric or colorimetric patterns