max planck institut
informatik

# 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},