BROADCASTING IN BUS INTERCONNECTION NETWORKS

2000 ◽  
Vol 01 (02) ◽  
pp. 73-94
Author(s):  
A. FERREIRA ◽  
A. GOLDMAN ◽  
S. W. SONG
Keyword(s):  
Interconnection Networks ◽  
High Performance ◽  
Interconnection Network ◽  
Parallel Architectures ◽  
Interprocessor Communication ◽  
Efficient Manner ◽  
Graph Theoretic ◽  
Communication Algorithms ◽  
Communication Links ◽  
Point To Point

In most distributed memory MIMD multiprocessors, processors are connected by a point-to-point interconnection network, usually modeled by a graph where processors are nodes and communication links are edges. Since interprocessor communication frequently constitutes serious bottlenecks, several architectures were proposed that enhance point-to-point topologies with the help of multiple bus systems so as to improve the communication efficiency. In this paper we study parallel architectures where the communication means are constituted solely by buses. These architectures can use the power of bus technologies, providing a way to interconnect much more processors in a simple and efficient manner. We present the hyperpath, hypergrid, hyperring, and hypertorus architectures, which are the bus-based versions of the well used point-to-point interconnection networks. Using (hyper) graph theoretic concepts to model inter-processor communication in such networks, we give optimal algorithms for broadcasting a message from one processor to all the others. For deriving high performance communication patterns we developed a new tool called simplification. The idea is to construct a graph, to be called representative graph, from the original hyper-topology, in such a way that it will become easy to describe and perform communication schemes to the former that will fit to the latter, because the simplification concept also allows us to partially use some already known communication algorithms for usual networks.

scholarly journals Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

2015 ◽  
Vol 25 (4) ◽  
pp. 723-735 ◽  
Author(s):  
Antoine Bossard ◽  
Keiichi Kaneko
Keyword(s):  
Interconnection Networks ◽  
High Performance ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Hamiltonian Path ◽  
Small Diameter ◽  
Critical Parameters ◽  
Time Optimal ◽  
Point To Point ◽  
Torus Networks

Abstract Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.

THE CUBE-OF-RINGS INTERCONNECTION NETWORK

1998 ◽  
Vol 09 (01) ◽  
pp. 25-37 ◽  
Author(s):  
THOMAS J. CORTINA ◽  
ZHIWEI XU
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Parallel Computers ◽  
Closed Form Expression ◽  
Form Expression ◽  
Graph Theoretic ◽  
Basic Graph

We present a family of interconnection networks named the Cube-Of-Rings (COR) networks along with their basic graph-theoretic properties. Aspects of group graph theory are used to show the COR networks are symmetric and optimally fault tolerant. We present a closed-form expression of the diameter and optimal one-to-one routing algorithm for any member of the COR family. We also discuss the suitability of the COR networks as the interconnection network of scalable parallel computers.

FACILITATING HIGH-PERFORMANCE IMAGE ANALYSIS ON REDUCED HYPERCUBE (RH) PARALLEL COMPUTERS

1995 ◽  
Vol 09 (04) ◽  
pp. 679-698 ◽  
Author(s):  
SOTIRIOS G. ZIAVRAS ◽  
MICHALIS A. SIDERAS
Keyword(s):  
Image Analysis ◽  
Interconnection Networks ◽  
High Performance ◽  
Interconnection Network ◽  
Parallel Computers ◽  
Number Of Publications ◽  
Low Dimensional ◽  
High Level ◽  
The Cost ◽  
Cube Connected Cycles

The direct binary hypercube interconnection network has been very popular for the design of parallel computers, because it provides a low diameter and can emulate efficiently the majority of the topologies frequently employed in the development of algorithms. The last fifteen years have seen major efforts to develop image analysis algorithms for hypercube-based parallel computers. The results of these efforts have culminated in a large number of publications included in prestigious scholarly journals and conference proceedings. Nevertheless, the aforementioned powerful properties of the hypercube come at the cost of high VLSI complexity due to the increase in the number of communication ports and channels per PE (processing element) with an increase in the total number of PE’s. The high VLSI complexity of hypercube systems is undoubtedly their dominant drawback; it results in the construction of systems that contain either a large number of primitive PE’s or a small number of powerful PE’s. Therefore, low-dimensional k-ary n-cubes with lower VSLI complexity have recently drawn the attention of many designers of parallel computers. Alternative solutions reduce the hypercube’s VLSI complexity without jeopardizing its performance. Such an effort by Ziavras has resulted in the introduction of reduced hypercubes (RH’s). Taking advantage of existing high-performance routing techniques, such as wormhole routing, an RH is obtained by a uniform reduction in the number of edges for each hypercube node. An RH can also be viewed as several connected copies of the well-known cube-connected-cycles network. The objective here is to prove that parallel computers comprising RH interconnection networks are definitely good choices for all levels of image analysis. Since the exact requirements of high-level image analysis are difficult to identify, but it is believed that versatile interconnection networks, such as the hypercube, are suitable for relevant tasks, we investigate the problem of emulating hypercubes on RH’s. The ring (or linear array), the torus (or mesh), and the binary tree are the most frequently used topologies for the development of algorithms in low-level and intermediate-level image analysis. Thus, to prove the viability of the RH for the two lower levels of image analysis, we introduce techniques for embedding the aforementioned three topologies into RH’s. The results prove the suitability of RH’s for all levels of image analysis.

A Note on the Nature Diagnosability of Alternating Group Graphs Under the PMC Model and MM* Model

2018 ◽  
Vol 18 (01) ◽  
pp. 1850005 ◽  
Author(s):  
SHIYING WANG ◽  
LINGQI ZHAO
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Alternating Group ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Free Node ◽  
Pmc Model ◽  
Important Study ◽  
Communication Links ◽  
Alternating Group Graph

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No faulty set can contain all the neighbors of any fault-free node in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we prove the following. (1) The nature diagnosability of AGn is 4n − 10 for n − 5 under the PMC model and MM* model. (2) The nature diagnosability of the 4-dimensional alternating group graph AG4 under the PMC model is 5. (3) The nature diagnosability of AG4 under the MM* model is 4.

Energy-Efficient Optical Interconnects in Cloud Computing Infrastructures

2013 ◽  
pp. 463-478
Author(s):  
Christoforos Kachris ◽  
Ioannis Tomkos
Keyword(s):  
Cloud Computing ◽  
Power Consumption ◽  
Interconnection Networks ◽  
Optical Interconnects ◽  
High Performance ◽  
Interconnection Network ◽  
Research Literature ◽  
Optical Interconnection ◽  
High Bandwidth ◽  
Cloud Infrastructures

This chapter discusses the rise of optical interconnection networks in cloud computing infrastructures as a novel alternative to current networks based on commodity switches. Optical interconnects can significantly reduce the power consumption and meet the future network traffic requirements. Additionally, this chapter presents some of the most recent and promising optical interconnects architectures for high performance data centers that have appeared recently in the research literature. Furthermore, it presents a qualitative categorization of these schemes based on their main features such as performance, connectivity, and scalability, and discusses how these architectures could provide green cloud infrastructures with reduced power consumption. Finally, the chapter presents a case study of an optical interconnection network that is based on high-bandwidth optical OFDM links and shows the reduction of the energy consumption that it can achieve in a typical data center.

Fault-Tolerant Maximal Local-Connectivity on Cayley Graphs Generated by Transpositions

2019 ◽  
Vol 30 (08) ◽  
pp. 1301-1315 ◽  
Author(s):  
Liqiong Xu ◽  
Shuming Zhou ◽  
Weihua Yang
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Cayley Graphs ◽  
Disjoint Paths ◽  
Local Connectivity ◽  
Communication Links ◽  
Restricted Condition ◽  
Vertex Disjoint

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A graph [Formula: see text] is said to be maximally local-connected if each pair of vertices [Formula: see text] and [Formula: see text] are connected by [Formula: see text] vertex-disjoint paths. In this paper, we show that Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected and are also [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have a triangle, [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have no triangles. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected if their corresponding transposition generating graphs have no triangles.

scholarly journals Variable Expanding Structure for Data Center Interconnection Networks

2021 ◽  
Vol 25 (1) ◽  
pp. 13-22
Author(s):  
Jianfei Zhang ◽  
◽  
Yuchen Jiang ◽  
Yan Liu
Keyword(s):  
Data Center ◽  
Interconnection Networks ◽  
High Performance ◽  
Large Scale ◽  
Data Centers ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Address Space ◽  
Novel Structure ◽  
Large Scale Data Processing

Data centers are fundamental facilities that support high-performance computing and large-scale data processing. To guarantee that a data center can provide excellent properties of expanding and routing, the interconnection network of a data center should be designed elaborately. Herein, we propose a novel structure for the interconnection network of data centers that can be expanded with a variable coefficient, also known as a variable expanding structure (VES). A VES is designed in a hierarchical manner and built iteratively. A VES can include hundreds of thousands and millions of servers with only a few layers. Meanwhile, a VES has an extremely short diameter, which implies better performance on routing between every pair of servers. Furthermore, we design an address space for the servers and switches in a VES. In addition, we propose a construction algorithm and routing algorithm associated with the address space. The results and analysis of simulations verify that the expanding rate of a VES depends on three factors: n, m, and k where the n is the number of ports on a switch, the m is the expanding speed and the k is the number of layers. However, the factor m yields the optimal effect. Hence, a VES can be designed with factor m to achieve the expected expanding rate and server scale based on the initial planning objectives.

scholarly journals The Edge Connectivity of Expanded k-Ary n-Cubes

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Shiying Wang ◽  
Mujiangshan Wang
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Complex Problem ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Complex Problem Solving ◽  
Edge Connectivity ◽  
Communication Links ◽  
Minimum Number

Mass data processing and complex problem solving have higher and higher demands for performance of multiprocessor systems. Many multiprocessor systems have interconnection networks as underlying topologies. The interconnection network determines the performance of a multiprocessor system. The network is usually represented by a graph where nodes (vertices) represent processors and links (edges) represent communication links between processors. For the network G, two vertices u and v of G are said to be connected if there is a (u,v)-path in G. If G has exactly one component, then G is connected; otherwise G is disconnected. In the system where the processors and their communication links to each other are likely to fail, it is important to consider the fault tolerance of the network. For a connected network G=(V,E), its inverse problem is that G-F is disconnected, where F⊆V or F⊆E. The connectivity or edge connectivity is the minimum number of F. Connectivity plays an important role in measuring the fault tolerance of the network. As a topology structure of interconnection networks, the expanded k-ary n-cube XQnk has many good properties. In this paper, we prove that (1) XQnk is super edge-connected (n≥3); (2) the restricted edge connectivity of XQnk is 8n-2 (n≥3); (3) XQnk is super restricted edge-connected (n≥3).

A New Unicast Routing Algorithm for Hyper Hexa-Cell Interconnection Networks

2017 ◽  
Vol 8 (3) ◽  
pp. 45-57
Author(s):  
Jehad Ahmed Al-Sadi
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Optimal Path ◽  
Destination Node ◽  
Topological Properties ◽  
Unicast Routing ◽  
Cell Topology ◽  
Store And Forward ◽  
Point To Point

The Hyper Hexa-Cell topology; HHC for short; is a new interconnection network topology that has many attractive topological properties compared to other traditional topologies. There have been a number of studies in the literature on the HHC to explore the promising topological properties of this topology. Furthermore, other studies extend this topology by combining it with OTIS technology to produce a new version called OHHC. We have found that there is a lake of presenting any point to point routing algorithm for the HHC, although there were some efforts on building routing algorithms for the OHHC. To cover this shortage, this paper introduces a new unicast routing algorithm for the HHC. The new routing algorithm for the HHC uses store-and-forward technique which allows a message to be transmitted through a path from the source node to the destination node. In addition to presenting the routing algorithm, we present an example to explore the algorithm steps and also an enhancement on the routing algorithm to apply adaptively on the routing based on parameterized criteria. Finally, we present a theoretical theorem to prove that the algorithm routes any message from any source to any destination via an optimal path.

Energy-Efficient Optical Interconnects in Cloud Computing Infrastructures

2013 ◽  
pp. 224-240 ◽  
Author(s):  
Christoforos Kachris ◽  
Ioannis Tomkos
Keyword(s):  
Cloud Computing ◽  
Power Consumption ◽  
Interconnection Networks ◽  
Optical Interconnects ◽  
High Performance ◽  
Interconnection Network ◽  
Research Literature ◽  
Optical Interconnection ◽  
High Bandwidth ◽  
Cloud Infrastructures

This chapter discusses the rise of optical interconnection networks in cloud computing infrastructures as a novel alternative to current networks based on commodity switches. Optical interconnects can significantly reduce the power consumption and meet the future network traffic requirements. Additionally, this chapter presents some of the most recent and promising optical interconnects architectures for high performance data centers that have appeared recently in the research literature. Furthermore, it presents a qualitative categorization of these schemes based on their main features such as performance, connectivity, and scalability, and discusses how these architectures could provide green cloud infrastructures with reduced power consumption. Finally, the chapter presents a case study of an optical interconnection network that is based on high-bandwidth optical OFDM links and shows the reduction of the energy consumption that it can achieve in a typical data center.

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