Abstract
This paper shows nontrivial ways to use the Reconfigurable Mesh to solve several basic arithmetic problems in constant time. These solutions are obtained by novel ways to represent numbers and by exploiting the reconfigurability of the architecture. In particular, a constant time algorithm to add nk-bit numbers using an n × nk bit model of Reconfigurable Mesh is shown. Using these techniques, an optimal sorting algorithm on the Reconfigurable Mesh is derived. The algorithm sorts n numbers in constant time using n × n processors. Our algorithm uses optimal size-of the mesh to sort n numbers in constant time and satisfies the AT 2 lower bound of Ω( n 2) for sorting n numbers in a variation of the word model of VLSI. The sorting algorithm runs on all known variations of the Reconfigurable Mesh model.
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