max planck institut
informatik

# MPI-I-93-138

## Routing and sorting on circular arrays

### Sibeyn, Jop F.

MPI-I-93-138. September 1993, 20 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We analyze routing and sorting problems on circular processor arrays
with bidirectional connections. We assume that initially and finally
each PU holds $k \geq 1$ packets. On linear processor arrays the
routing and sorting problem can easily be solved for any $k$, but
for the circular array it is not obvious how to exploit the
wrap-around connection.

We show that on an array with $n$ PUs $k$-$k$ routing, $k \geq 4$,
can be performed optimally in $k \cdot n / 4 + \sqrt{n}$ steps by a
deterministical algorithm. For $k = 1$, the routing problem is
trivial. For $k = 2$ and $k = 3$, we prove lower-bounds and show
that these (almost) can be matched. A very simple algorithm has
good performance for dynamic routing problems.

For the $k$-$k$ sorting problem we use a powerful algorithm which
also can be used for sorting on higher-dimensional tori and meshes.
For the ring the routing time is $\max\{n, k \cdot n / 4\} + {\cal O}((k \cdot n)^{2/3})$ steps. For large $k$ we take the computation
time into account and show that for $n = o(\log k)$ optimal speed-up
can be achieved. For $k < 4$, we give specific results, which
come close to the routing times.
Acknowledgement:
References to related material:

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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1993-138
BibTeX
@TECHREPORT{Sibeyn93,
AUTHOR = {Sibeyn, Jop F.},
TITLE = {Routing and sorting on circular arrays},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},