Abstract
A class of interconnection networks for massively parallel processors are designed by taking copies of a building block network and wiring them together. For Dragonfly networks, the building block network is a complete graph and the wiring together is done by either a cycle or a complete graph. The process may be viewed as a way to construct a new graph from two component graphs.The resulting graph is known as a replacement graph. Furthermore, one of these constructions leads to a very large number of graphs, some of which are provably not isomorphic. The point is that the construction of a replacement in G by H requires that G be converted to a network. This paper explains the way the graph of an interconnection network is labeled and a table which is analogous to the adjacency matrix of a labeled graph. The table is used to demonstrate the nondeterminism of the concept of a replacement graph. The graph constructions are presented along with the motivating interconnection networks. The graph constructions can be generalized.
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Notes
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If global ports do not permute the groups, a source vector using a global port that sends two groups to one group can lead to a local link collision. This can lead to algorithms which generate hot spots.
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Draper, R. (2024). Graph Constructions Derived from Interconnection Networks. In: Hoffman, F., Holliday, S., Rosen, Z., Shahrokhi, F., Wierman, J. (eds) Combinatorics, Graph Theory and Computing. SEICCGTC 2021. Springer Proceedings in Mathematics & Statistics, vol 448. Springer, Cham. https://doi.org/10.1007/978-3-031-52969-6_15
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DOI: https://doi.org/10.1007/978-3-031-52969-6_15
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