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Combinatorica

, Volume 21, Issue 1, pp 95–138 | Cite as

Deterministic Routing With Bounded Buffers: Turning Offline Into Online Protocols

  • Friedhelm Meyer auf der Heide
  • Christian Scheideler
Original Paper

In this paper we present a deterministic protocol for routing arbitrary permutations in arbitrary networks. The protocol is analyzed in terms of the size of the network and the routing number of the network. Given a network H of n nodes, the routing number of H is defined as the maximum over all permutations \(\) on {1, ..., n} of the minimal number of steps to route \(\) offline in H. We show that for any network H of size n with routing number R our protocol needs \(\) time to route any permutation in H using only constant size edge buffers. This significantly improves all previously known results on deterministic routing. In particular, our result yields optimal deterministic routing protocols for arbitrary networks with diameter \(\) or bisection width \(\), \(\) constant. Furthermore we can extend our result to deterministic compact routing. This yields, e.g., a deterministic routing protocol with runtime O(R logn) for arbitrary bounded degree networks if only O(logn) bits are available at each node for storing routing information.

Our protocol is a combination of a generalized ``routing via simulation'' technique with an new deterministic protocol for routing h-relations in an extended version of a multibutterfly network. This protocol improves upon all previous routing protocols known for variants of the multibutterfly network. The ``routing via simulation'' technique used here extends a method previously introduced by the authors for designing compact routing protocols.

AMS Subject Classification (1991) Classes:  68W10, 68W15, 68W20 

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Copyright information

© János Bolyai Mathematical Society, 2001

Authors and Affiliations

  • Friedhelm Meyer auf der Heide
    • 1
  • Christian Scheideler
    • 2
  1. 1.Department of Mathematics and Computer Science, and Heinz Nixdorf Institute, University of Paderborn; 33095 Paderborn, Germany; E-mail: fmadh@uni-paderhorn.deDE
  2. 2.Department of Comuter Science, Johns Hopkins University; 3400 N. Charles Street Baltimore, MD 21218–2682 USA; E-mail: scheideler@cs.jhu.eduUS

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