Bounds on the Diameter of One-Dimensional PEC Networks

Abstract The diameter of a packed exponential connections (PEC) network on N nodes is shown to be Θ([formula] × [formula]).4 A routing algorithm which can route between any two nodes in O([formula] × [formula]) steps is shown. A methodology to find a set of links to be used by a shortest path from node 1 to node N − 1 is derived. We also show that semigroup operations can be performed in O([formula] × [formula]) parallel steps.