A unified approach to off-line permutation routing on parallel networks

A Note on Off-Line Permutation Routing on a Mesh-Connected Processor Array

“…Recall how Annexstein and Blaumslag [1] perform off-line permutation routing on the mesh. They show that any permutation can be realized by first performing a permutation of each of the rows, followed by a permutation of the columns and finishing with another permutation of the rows.…”

“…(The number is constant but estimated to be in excess of 500.) As a corollary to one of their theorems, Annexstein and Blaumslag [1] show how to off-line route in 3n -3 steps with at most 3 packets per processor. In this note we extend this result by showing that by allowing only a slight increase in the amount of storage required a great improvement in the time can be made.…”

Permutation routing via Cayley graphs with an example for bus interconnection networks

“…There has been an extensive literature on the use of Cayley graphs to design interconnection networks [1,2,5,6,7,12]. Cayley graphs have been used extensively to study point-to-point routing, and they have been particularly attractive for the degree-diameter problem [3,5,7].…”

“…This paper describes the use of Cayley graphs to study permutation routing. There are also other approaches to permutation routing [1,11] that concentrate more on heuristics and an overall framework.…”

“…Cayley graphs have been used extensively to design interconnection networks and provide a natural setting for studying point-to-point routing [1,2,3,5,6,7,12]. The extension of these techniques to the more important problem of permutation routing on interconnection networks presents fundamental problems.…”