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The Computer Journal 2000 43(3):243-249; doi:10.1093/comjnl/43.3.243
© 2000 by British Computer Society
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On the Dilation of Interval Routing

Cyril Gavoille1

1 LaBRI, Universitè. Bordeaux I, 351, cours de la Libè.ration, 33405 Talence Cedex, France Email: gavoille@labri.u-bordeaux.fr

In this paper we deal with interval routing on $n$-node networks of diameter $D$. We show that, for all $n$ and $D$ such that $2 \leq D \leq \Theta(n)$, there exists a network on which every interval routing scheme with less than $\Omega(n/(D\log (n/D)))$ intervals per link has a routing path length at least $\lfloor 3D/2\rfloor-1$. It improves the lower bound on the routing path lengths for the range of a very large number of intervals. Moreover, we build a network of bounded degree, for all $n$ and $D$ such that $\Theta(\log n) \leq D \leq \Theta(n)$, on which every interval routing scheme with less than $\Omega(n/D^2)$ intervals per link has a routing path length at least $3D/2 - O(\log n)$.

Received 6 December, 2000. Revised 31 May, 2000.


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