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

##### MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45478

Sibeyn,  Jop
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44745

Kaufmann,  Michael
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

##### Externe Ressourcen
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##### Volltexte (frei zugänglich)

MPI-I-93-163.pdf
(beliebiger Volltext), 233KB

##### Ergänzendes Material (frei zugänglich)
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##### Zitation

Sibeyn, J., & Kaufmann, M.(1993). Deterministic 1-k routing on meshes with applications to worm-hole routing (MPI-I-93-163). Saarbrücken: Max-Planck-Institut für Informatik.

In $1$-$k$ routing each of the $n^2$ processing units of an $n \times n$ 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 reflects practical desire for routing better than the popular routing of permutations. $1$-$k$ routing also has implications for hot-potato worm-hole routing, which is of great importance for real world systems. We present a near-optimal deterministic algorithm running in $\sqrt{k} \cdot n / 2 + \go{n}$ steps. We give a second algorithm with slightly worse routing time but working queue size three. Applying this algorithm considerably reduces the routing time of hot-potato worm-hole routing. Non-trivial extensions are given to the general $l$-$k$ routing problem and for routing on higher dimensional meshes. Finally we show that $k$-$k$ routing can be performed in $\go{k \cdot n}$ steps with working queue size four. Hereby the hot-potato worm-hole routing problem can be solved in $\go{k^{3/2} \cdot n}$ steps.