Chordal Topologies for Interconnection Networks

Beivide, Ramón; Martínez, Carmen; Izu, Cruz; Gutiérrez, Jaime; Gregorio, J.A.; Miguel-Alonso, José

doi:10.1007/978-3-540-39707-6_33

Cited by 14 publications

(4 citation statements)

References 15 publications

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“…By adding the reachable nodes at distances 1 through k 2 the expression 2k 2 + 2k + 1 is obtained, which gives the number of nodes in the dense mesh-based graph of diameter k. Note that it is more than twice the number nodes in a common 2D torus, meaning that it is far from being dense. Dense tori were deeply studied in [24]. The same conclusion can be reached when considering the degree six, diagonal networks.…”

Section: King Networkmentioning

confidence: 55%

Assessing the Suitability of King Topologies for Interconnection Networks

Stafford

Bosque

Martínez

et al. 2016

IEEE Trans. Parallel Distrib. Syst.

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In the late years many different interconnection networks have been used with two main tendencies. One is characterized by the use of high-degree routers with long wires while the other uses routers of much smaller degree. The latter rely on two-dimensional mesh and torus topologies with shorter local links. This paper focuses on doubling the degree of common 2D meshes and tori while still preserving an attractive layout for VLSI design. By adding a set of diagonal links in one direction, diagonal networks are obtained. By adding a second set of links, networks of degree eight are built, named king networks. This research presents a comprehensive study of these networks which includes a topological analysis, the proposal of appropriate routing procedures and an empirical evaluation. King networks exhibit a number of attractive characteristics which translate to reduced execution times of parallel applications. For example, the execution times NPB suite are reduced up to a 30%. In addition, this work reveals other properties of king networks such as perfect partitioning that deserves further attention for its convenient exploitation in forthcoming high-performance parallel systems.

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Section: King Networkmentioning

confidence: 55%

Assessing the Suitability of King Topologies for Interconnection Networks

Stafford

Bosque

Martínez

et al. 2016

IEEE Trans. Parallel Distrib. Syst.

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“…Martinez et al [13,24] applied circulant networks, in particular a family of type ( ), in coding theory when constructing perfect group codes. The implementation of the graphs described by (1) or (2) was proposed as a topology in the design of supercomputers with mass parallelism and NoCs [5,23,25]. A number of new hierarchical network designs were also constructed using the Minimum Distance Mesh with Wrap-around links (Midimew networks) as elements [26,27]; simple use of circulant (Midimew) topologies instead torus topology in TESH [28] topology notably improved network performance parameters [29].…”

Section: Optimal Two-dimensional Circulantsmentioning

confidence: 99%

Shortest Path Search Algorithm in Optimal Two-Dimensional Circulant Networks: Implementation for Networks-on-Chip

2020

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“…Applications of chordal rings to parallel systems started very early in the history of parallel processing and have continued to date [18], [38], although in some cases the interconnection structures include subtle variations and carry different names, thus making it difficult to identify the underlying chordal ring networks. The bulk of studies of chordal rings in relation to interconnection networks deal with networks of small, fixed node degrees; most commonly, 3-6 for undirected (4 being most heavily studied [5], [9], [11]), and 2-3 for directed networks [34], [35]. The rich mathematical properties of chordal rings has also attracted numerous theoretical studies, some without explicit or immediate applications.…”

Section: Related Workmentioning

confidence: 99%

Periodically Regular Chordal Rings Are Preferable to Double-Ring Networks

Parhami

2008

J. Inter. Net.

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The susceptibility of ring networks to disconnection as a result of one or two node/link failures has led to a number of proposals to increase the robustness of such networks. One class of proposals, discussed primarily in the networking and communication communities, but also advocated for use in parallel and distributed systems, involves the provision of a second ring to improve system throughput during nonnal operation and to make alternate paths available in the event of node or link failures. With regard to the advantages just listed, chordal rings are quite similar to double-ring networks, and periodically regular chordal (PRC) rings offer the added benefit of smaller node degree compared with node-symmetric chordal rings of comparable diameters. In this paper, we note that certain double-ring networks are isomorphic to suitably constructed PRC rings, while other varieties correspond to PRC rings that closely approximate their static and dynamic attributes. These results, combined with greater flexibility and other advantages for the PRC-ring family of networks, demonstrate that PRC rings are preferable to double-ring networks in virtually all application contexts. A byproduct of our observations on the relationships among double-ring networks, generalized Petersen graphs, and PRC rings is that by amalgamating known results for these network classes, many more tools and techniques become applicable to the analysis and synthesis of robust ring networks for parallel and distributed computing. As examples of new results that can be developed with this viewpoint, we present near-optimal and fault-tolerant routing algorithms for our PRC ring networks.

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Chordal Topologies for Interconnection Networks

Cited by 14 publications

References 15 publications

Assessing the Suitability of King Topologies for Interconnection Networks

Assessing the Suitability of King Topologies for Interconnection Networks

Shortest Path Search Algorithm in Optimal Two-Dimensional Circulant Networks: Implementation for Networks-on-Chip

Periodically Regular Chordal Rings Are Preferable to Double-Ring Networks

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