MPI-INF/SWS Research Reports 1991-2021

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

Sibeyn, Jop F. and Kaufmann, Michael

November 1993, 13 pages.

Status: available - back from printing

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},