Deterministic 1 -k routing on meshes with applications to worm-hole routing

  • Jop F. Sibeyn
  • Michael Kaufmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)


In 1-k routing each of the n2 processing units of an n x n mesh connected computer initially holds 1 packet which must be routed such that any processor is the destination of at most k packets. This problem has great practical importance in itself and by its implications for hot-potato worm-hole routing.

We present a near-optimal deterministic algorithm running in \(\sqrt k \cdot {n \mathord{\left/{\vphantom {n 2}} \right.\kern-\nulldelimiterspace} 2} + \mathcal{O}\left( n \right)\) steps, and an algorithm with slightly worse routing time but working queue size three. Non-trivial extensions are given to l-k routing, and for routing on higher dimensional meshes. We show that under a natural condition 1-k routing can be performed in \(\mathcal{O}\left( n \right)\) steps. Finally we show that k-k routing can be performed in \(\mathcal{O}\left( {k \cdot n} \right)\) steps with working queue size four. Hereby hot-potato worm-hole routing can be performed in \(\mathcal{O}\left( {k^{{3 \mathord{\left/{\vphantom {3 2}} \right.\kern-\nulldelimiterspace} 2}} \cdot n} \right)\) steps.


theory of parallel and distributed computation meshes packet routing hot-potato worm-hole routing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jop F. Sibeyn
    • 1
  • Michael Kaufmann
    • 2
  1. 1.Max-Planck-Institut für Informatik Im StadtwaldSaarbrückenGermany
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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