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Direct routing: Algorithms and complexity

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Abstract

Direct routing is the special case ofbufferless routing whereN packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing:

  1. 1.

    Algorithms. We present a polynomial-timegreedy direct algorithm which is worst-case optimal. We improve the bound of the greedy algorithm for special cases, by applying variants of this algorithm to commonly used network topologies. In particular, we obtainnear-optimal routing time for thetree, mesh, butterfly, andhypercube.

  2. 2.

    Complexity. By a reduction from Vertex Coloring, we show that optimal Direct Routing is inapproximable, unless P=NP.

  3. 3.

    Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; in order to solve these problems,any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms.

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Authors and Affiliations

  1. Department of Computer Science, Rensselaer Polytechnic Institute, 110 8th Street, 12180, Troy, NY, USA

    Costas Busch & Malik Magdon-Ismail

  2. Department of Computer Science, University of Cyprus, P.O. Box 20537, CY-1678, Nicosia, Cyprus

    Marios Mavronicolas

  3. Department of Computer Engineering and Informatics, University of Patras, Rion, 265 00, Patras, Greece

    Paul Spirakis

  4. Computer Technology Institute, 61 Riga Fereou Street, 26221, Patras, Greece

    Paul Spirakis

Authors
  1. Costas Busch
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  2. Malik Magdon-Ismail
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  3. Marios Mavronicolas
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  4. Paul Spirakis
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Corresponding author

Correspondence to Costas Busch.

Additional information

A preliminary version of this paper appears in theProceedings of the 12th Annual European Symposium on Algorithms (ESA 2004) [11].

Partially supported by the EU within the 6th Framework Programme under Contract 001907 “Dynamically Evolving, Large Scale Information Systems” (DELIS).

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Busch, C., Magdon-Ismail, M., Mavronicolas, M. et al. Direct routing: Algorithms and complexity. Algorithmica 45, 45–68 (2006). https://doi.org/10.1007/s00453-005-1189-3

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  • DOI: https://doi.org/10.1007/s00453-005-1189-3

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