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Deadlock-free interval routing schemes

  • Parallel and Distributed Systems I
  • Conference paper
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STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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Abstract

k-Interval Labeling Schemes (k-ILS) are compact routing schemes on general networks which have been studied extensively and recently been implemented on the latest generation INMOS Transputer Router chips. In this paper we introduce an extension of the k-ILS to the 〈k, s∼>-DFILS (Deadlock-Free ILS), where k is the number of intervals and s is the number of buffers used at each node or edge to prevent deadlock. Whereas k-ILS only compactly represents shortest paths between pairs of nodes, this new extension aims to represent those particular ones that give rise also to deadlock-free routing controllers which use a low number of buffers per node or per edge. In this paper we prove new NP-hardness results on the problem of devising low occupancy schemes, also for classical k-ILS. Moreover, while space complexity results are given for 〈k, s∼>-DFILS in arbitrary networks, tight results are shown for specific topologies, such as trees, rings, grids, complete graphs and chordal rings. Finally, trade-offs are derived between the number of intervals k and the number of buffers s in Deadlock-Free Interval Routing Schemes for hypercubes, grids, tori and Cartesian products of graphs.

Work supported by the EU TMR Research Training Grant N. ERBFMBICT960861, by the EU ESPRIT Long Term Research Project ALCOM-IT under contract N. 20244 and by the Italian MURST 40% project “Algoritmi, Modelli di Calcolo e Strutture Informative”.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, University of L'Aquila, via Vetoio loc.Coppito, I-67100, L'Aquila, Italy

    Michele Flammini

  2. Project SLOOP I3S-CNRS/INRIA/Université de Nice-Sophia Antipolis, 930 route des Colles, F-06903, Sophia Antipolis Cedex, France

    Michele Flammini

Authors
  1. Michele Flammini
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Rüdiger Reischuk Michel Morvan

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© 1997 Springer-Verlag Berlin Heidelberg

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Flammini, M. (1997). Deadlock-free interval routing schemes. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023472

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  • DOI: https://doi.org/10.1007/BFb0023472

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

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