ATM layouts with bounded hop count and congestion

  • Michele Flammin
  • Enrico Nardelli
  • Guido Proietti
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1320)


In this paper we consider two new cost measures related to the communication overhead and the space requirements associated to virtual path layouts in ATM networks, that is the edge congestion and the node congestion. Informally, the edge congestion of a given edge e at an incident node u is defined as the number of VPs terminating or starting from e at u, while the node congestion of a node v is defined as the number of VPs having v as an endpoint. We investigate the problem of constructing virtual path layouts allowing to connect a specified root node to all the others in at most h hops and with maximum edge or node congestion c, for two given integers h and c. We first give tight results concerning the time complexity of the construction of such layouts for both the two congestion measures, that is we exactly determine all the tractable and intractable cases. Then, we provide some combinatorial bounds for arbitrary networks, together with optimal layouts for specific topologies such as chains, rings, grids and tori. Extensions to d-dimensional grids and tori with d > 2 are also discussed.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Michele Flammin
    • 1
    • 2
  • Enrico Nardelli
    • 1
    • 3
  • Guido Proietti
    • 1
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità degli Studi di L'AquilaL'AquilaItaly
  2. 2.Project SLOOP 13S-CNRS/INRIA/Université de Nice-Sophia AntipolisSophia Antipolis CedexFrance
  3. 3.Consiglio Nazionale delle RicercheIstituto di Analisi dei Sistemi ed InformativaRomaItaly

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