In this paper, we consider the problem of permutation routing in twoand three-dimensional mesh-connected processor arrays. We present new on-line and off-line routing algorithms, all of which are optimal to within a small additive term. In particular, our results include the following: 1. An off-line algorithm for routing a permutation in an n x n mesh in time 2n – 1 using buffers of size 4. 2. An off-line algorithm for routing a permutation in an n x n x n mesh in time 372– 1 using buffers of size 10. 3. An on-line randomized algorithm for routing a permutation in an n x n x n mesh in time 3n + O(log n) time using constant sized buffers, ●Supported in part by NSF Grant NSF-CCR-87-04513. This work was done while visiting NEC Research Institute. E-mail: kakl@harvard.harvard .edu t This work was done while visiting N EC Research Institute. E-mail: krizanc@cs. rochester.edu t E-mail: satish@research .nj.nec.com Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinety. To copy otherwise, or to republish, requires a fee and/or speeitic permission. SF’AA ’9261921CA @1992 ACM O-89791-484-8192K)O0610023. . . . . .. $1.50 23 4. An on-line randomized algorithm for routing a permutation in an n x n torus in time n + O(log n ) time using constant sized buffers. Also, while optimal algorithms for routing on two-dimensional meshes were known, we give new algorithms that are simpler and/or require smaller buffers.
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