Topologies for Optical Interconnection Networks Based on the Optical Transpose Interconnection System

International audienceMany results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be done in linking those results together. In this paper, we propose a step in this direction, by giving optical layouts for several graph-theoretical topologies studied in the literature, using the Optical Transpose Interconnection System (OTIS) architecture. These topologies include the family of Partitioned Optical Passive Star (POPS) and stack-Kautz networks as well as a generalization of the Kautz and de Bruijn digraphs

OTIS-Based Multi-Hop Multi-OPS Lightwave Networks

International audienceAdvances in optical technology, such as low loss Optical Passive Star couplers (OPS) and the possibility of building tunable optical transmitters and receivers have increased the interest for multiprocessor architectures based on lightwave networks because of the vast bandwidth available. Many research have been done at both technological and theoretical level. An essential effort has to be done in linking those results. In this paper we propose optical designs for two multi-OPS networks: the single-hop POPS network and the multi-hop stack-Kautz network; using the Optical Transpose Interconnecting System (OTIS) architecture, from the Optoelectronic Computing Group of UCSD. In order to achieve our result, we also provide the optical design of a generalization of the Kautz digraph, using OTIS

Efficient algorithms for the optical multi-trees (OMULT) architecture.

In this thesis, we have reported our investigations on efficiently implementing algorithms on the recently proposed Optical Multi-Trees (OMULT) multi-processors interconnection architecture that uses both electronic and optical links among processors. We have investigated algorithms for matrix multiplication of two matrices of size n2 x n2 and two matrices of arbitrary size, the prefix-sum of a series and some fundamental computational geometry problems. We show that some common algorithms for computational geometry---finding the convex hull, the smallest enclosing box, the empirical cumulative distribution function and the all-nearest neighbor problems of n data points can be computed on the OMULT network in O(log n) time, compared to O(√n) algorithms on the Optical Transpose Interconnection System (OTIS) mesh for each of these problems. Finally we have implemented our algorithm for matrix multiplication using the SimJava simulation tool and feel that this is a convenient environment for testing such parallel algorithms.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .I85. Source: Masters Abstracts International, Volume: 43-05, page: 1751. Adviser: Subir Bandyopadhyay. Thesis (M.Sc.)--University of Windsor (Canada), 2004

Topologies for Optical Interconnection Networks Based on the Optical Transpose Interconnection System

International audienceMany results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be done in linking those results together. In this paper, we propose a step in this direction, by giving optical layouts for several graph-theoretical topologies studied in the literature, using the Optical Transpose Interconnection System (OTIS) architecture. These topologies include the family of Partitioned Optical Passive Star (POPS) and stack-Kautz networks as well as a generalization of the Kautz and de Bruijn digraphs

Theoretical Aspects of the Optical Transpose Interconnecting System Architecture

National audienceAn attractive way of implementing efficient local interconnection networks is to use the Optical Transpose Interconnecting System (OTIS) architecture proposed in [8]. This system allows to optically interconnect some set of processors in a Free Space of Optical Interconnections (FSOI). Briefly, it consists of two lenslet arrays allowing a large number of optical interconnections from a set of transmitters to a set of receivers. Note that the OTIS architecture is indeed a three dimension (3D) one but it can always be modeled in a 2D-space. We first try to provide ways of determining if a given general network admits an OTIS layout or not. Then we study particular case of regular and symmetric networks. Finally we show that classical topologies like de Bruijn, Kautz and complete digraphs admit an OTIS2D -layout. At the end, the results obtained for the OTIS2D model are applied to the OTIS3D case

Some studies on the multi-mesh architecture.

In this thesis, we have reported our investigations on interconnection network architectures based on the idea of a recently proposed multi-processor architecture, Multi-Mesh network. This includes the development of a new interconnection architecture, study of its topological properties and a proposal for implementing Multi-Mesh using optical technology. We have presented a new network topology, called the 3D Multi-Mesh (3D MM) that is an extension of the Multi-Mesh architecture [DDS99]. This network consists of n3 three-dimensional meshes (termed as 3D blocks), each having n3 processors, interconnected in a suitable manner so that the resulting topology is 6-regular with n6 processors and a diameter of only 3n. We have shown that the connectivity of this network is 6. We have explored an algorithm for point-to-point communication on the 3D MM. It is expected that this architecture will enable more efficient algorithm mapping compared to existing architectures. We have also proposed some implementation of the multi-mesh avoiding the electronic bottleneck due to long copper wires for communication between some processors. Our implementation considers a number of realistic scenarios based on hybrid (optical and electronic) communication. One unique feature of this investigation is our use of WDM wavelength routing and the protection scheme. We are not aware of any implementation of interconnection networks using these techniques.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .A32. Source: Masters Abstracts International, Volume: 43-03, page: 0868. Adviser: Subir Bandyopadhyay. Thesis (M.Sc.)--University of Windsor (Canada), 2004

Multiswapped networks and their topological and algorithmic properties

We generalise the biswapped network Bsw(G)Bsw(G) to obtain a multiswapped network Msw(H;G)Msw(H;G), built around two graphs G and H. We show that the network Msw(H;G)Msw(H;G) lends itself to optoelectronic implementation and examine its topological and algorithmic. We derive the length of a shortest path joining any two vertices in Msw(H;G)Msw(H;G) and consequently a formula for the diameter. We show that if G has connectivity κ⩾1κ⩾1 and H has connectivity λ⩾1λ⩾1 where λ⩽κλ⩽κ then Msw(H;G)Msw(H;G) has connectivity at least κ+λκ+λ, and we derive upper bounds on the (κ+λ)(κ+λ)-diameter of Msw(H;G)Msw(H;G). Our analysis yields distributed routing algorithms for a distributed-memory multiprocessor whose underlying topology is Msw(H;G)Msw(H;G). We also prove that if G and H are Cayley graphs then Msw(H;G)Msw(H;G) need not be a Cayley graph, but when H is a bipartite Cayley graph then Msw(H;G)Msw(H;G) is necessarily a Cayley graph

Efficient structural outlooks for vertex product networks

In this thesis, a new classification for a large set of interconnection networks, referred to as "Vertex Product Networks" (VPN), is provided and a number of related issues are discussed including the design and evaluation of efficient structural outlooks for algorithm development on this class of networks. The importance of studying the VPN can be attributed to the following two main reasons: first an unlimited number of new networks can be defined under the umbrella of the VPN, and second some known networks can be studied and analysed more deeply. Examples of the VPN include the newly proposed arrangement-star and the existing Optical Transpose Interconnection Systems (OTIS-networks). Over the past two decades many interconnection networks have been proposed in the literature, including the star, hyperstar, hypercube, arrangement, and OTIS-networks. Most existing research on these networks has focused on analysing their topological properties. Consequently, there has been relatively little work devoted to designing efficient parallel algorithms for important parallel applications. In an attempt to fill this gap, this research aims to propose efficient structural outlooks for algorithm development. These structural outlooks are based on grid and pipeline views as popular structures that support a vast body of applications that are encountered in many areas of science and engineering, including matrix computation, divide-and- conquer type of algorithms, sorting, and Fourier transforms. The proposed structural outlooks are applied to the VPN, notably the arrangement-star and OTIS-networks. In this research, we argue that the proposed arrangement-star is a viable candidate as an underlying topology for future high-speed parallel computers. Not only does the arrangement-star bring a solution to the scalability limitations from which the Abstract existing star graph suffers, but it also enables the development of parallel algorithms based on the proposed structural outlooks, such as matrix computation, linear algebra, divide-and-conquer algorithms, sorting, and Fourier transforms. Results from a performance study conducted in this thesis reveal that the proposed arrangement-star supports efficiently applications based on the grid or pipeline structural outlooks. OTIS-networks are another example of the VPN. This type of networks has the important advantage of combining both optical and electronic interconnect technology. A number of studies have recently explored the topological properties of OTIS-networks. Although there has been some work on designing parallel algorithms for image processing and sorting, hardly any work has considered the suitability of these networks for an important class of scientific problems such as matrix computation, sorting, and Fourier transforms. In this study, we present and evaluate two structural outlooks for algorithm development on OTIS-networks. The proposed structural outlooks are general in the sense that no specific factor network or problem domain is assumed. Timing models for measuring the performance of the proposed structural outlooks are provided. Through these models, the performance of various algorithms on OTIS-networks are evaluated and compared with their counterparts on conventional electronic interconnection systems. The obtained results reveal that OTIS-networks are an attractive candidate for future parallel computers due to their superior performance characteristics over networks using traditional electronic interconnects