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

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STACS 94 (STACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

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Abstract

In 1-k routing each of the n 2 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.

This research was partially supported by EC Cooperative Action IC-1000 (Project ALTEC: Algorithms for Future Technologies).

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Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

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© 1994 Springer-Verlag Berlin Heidelberg

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Sibeyn, J.F., Kaufmann, M. (1994). Deterministic 1 -k routing on meshes with applications to worm-hole routing. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_145

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  • DOI: https://doi.org/10.1007/3-540-57785-8_145

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