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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.
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  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},