A class of hierarchical graphs as topologies for interconnection networks

Lai, P.-L.; Hsu, H.-C.; Tsai, C.-H.; Stewart, I.A.

Abstract

We study some topological and algorithmic properties of a recently defined hierarchical interconnection network, the hierarchical crossed cube HCC(k,n), which draws upon constructions used within the well-known hypercube and also the crossed cube. In particular, we study: the construction of shortest paths between arbitrary vertices in HCC(k,n); the connectivity of HCC(k,n); and one-to-all broadcasts in parallel machines whose underlying topology is HCC(k,n) (with both one-port and multi-port store-and-forward models of communication). Moreover, (some of) our proofs are applicable not just to hierarchical crossed cubes but to hierarchical interconnection networks formed by replacing crossed cubes with other families of interconnection networks. As such, we provide a generic construction with accompanying generic results relating to some topological and algorithmic properties of a wide range of hierarchical interconnection networks.

Citation

Lai, P., Hsu, H., Tsai, C., & Stewart, I. (2010). A class of hierarchical graphs as topologies for interconnection networks. Theoretical Computer Science, 411(31-33), 2912-2924. https://doi.org/10.1016/j.tcs.2010.04.022

• Journal Article Type: Article
• Publication Date: Jun 1, 2010
• Deposit Date: Apr 12, 2010
• Publicly Available Date: Jun 2, 2010
• Journal: Theoretical Computer Science
• Print ISSN: 0304-3975
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 411
• Issue: 31-33
• Pages: 2912-2924
• DOI: https://doi.org/10.1016/j.tcs.2010.04.022
• Keywords: Interconnection networks, Hierarchical interconnection networks, Crossed cubes.
• Public URL: https://durham-repository.worktribe.com/output/1544891
• Publisher URL: http://www.dur.ac.uk/i.a.stewart/Papers/HierCrossedCubes.pdf