Pin-efficient networks for cubic neighborhoods

Pin-efficient bussed network families are discussed that can-in one clock tick-simultaneously shift all data in a k-dimensional grid to neighboring processors in any one of the 3^k-1 `compass directions´ x&oarr;→x&oarr;+δ&oarr;, for every nonzero vector δ&oarr; ∈ {-1,0,1}^k. The networks have the advantages of being simple to describe (using a single 5-state automaton), extendible (the k-dimensional network is obtained by extending the busses of the (k-1)-dimensional network), and provably optimal for k⩽3. The networks use only [3/2(√3)^k] pins per processor, which is within 3/2 of the theoretical minimum number of pins required. The best previously known family uses 2^k pins