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Concurrent flows and packet routing in Cayley graphs (Preliminary version)

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Graph-Theoretic Concepts in Computer Science (WG 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 790))

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Abstract

Let G be a Cayley graph on n vertices with degree D. We effectively compute a vertex optimal integral uniform concurrent flow in G and develop an offline packet routing algorithm for routing n(n−l) packets. The number of communication steps to route all packets to their destination is shown to be within a multiplicative factor of D from the optimum. Our algorithm can be implemented online in many existing parallel networks, so that the number of communication steps is within a multiplicative factor D from the optimum. Slight variations of our algorithm give rise to effective packet routing algorithms in perfect shuffles and deBruijn graphs. The model of computation required for our routing strategy may be assumed to be either MIMD or SIMD, as our online solutions only require the execution of the same instruction at the processors while routing.

Research of the second author was supported by the A. v. Humboldt-Stiftung while he was visiting at the Institut für diskrete Mathematik, Bonn; and by the U.S. Office of Naval Research under the contract N-0014-91-J-1385.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of North Texas, USA

    Farhad Shahrokhi

  2. Department of Computer Science, Eötvös University, USA

    Laszló A. Székely

Authors
  1. Farhad Shahrokhi
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  2. Laszló A. Székely
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Shahrokhi, F., Székely, L.A. (1994). Concurrent flows and packet routing in Cayley graphs (Preliminary version). In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_63

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  • DOI: https://doi.org/10.1007/3-540-57899-4_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57899-4

  • Online ISBN: 978-3-540-48385-4

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