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Using semidirect products of groups to build classes of interconnection networks.

Stewart, I.A. (2020) 'Using semidirect products of groups to build classes of interconnection networks.', Discrete applied mathematics., 283 . pp. 78-97.


We build a framework within which we can define a wide range of Cayley graphs of semidirect products of abelian groups, suitable for use as interconnection networks and which we call toroidal semidirect product graphs. Our framework encompasses various existing interconnection networks such as cube-connected cycles, recursive cubes of rings, cube-connected circulants and dual-cubes, as well as certain multiswapped networks, pruned tori and biswapped networks; it also enables the construction of new hitherto uninvestigated but highly structured interconnection networks. We go on to design an efficient shortest-path routing algorithm that can be applied to any graph that can be defined within our framework. Our algorithm runs in time that is polylogarithmic in the size of the base group and polynomial in the size of the extending group of the given semidirect product. We also obtain analytic upper bounds on the diameters of our toroidal semidirect product graphs.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:18 December 2019
Date deposited:03 January 2020
Date of first online publication:30 December 2020
Date first made open access:30 December 2020

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