# MPI-I-93-163

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

### Sibeyn, Jop F. and Kaufmann, Michael

**MPI-I-93-163**. November** **1993, 13 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1993-163

**BibTeX**
`@TECHREPORT{``SibeynKaufmann93``,`

` AUTHOR = {Sibeyn, Jop F. and Kaufmann, Michael},`

` TITLE = {Deterministic 1-k routing on meshes with applications to worm-hole routing},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-93-163},`

` MONTH = {November},`

` YEAR = {1993},`

` ISSN = {0946-011X},`

`}`