Chordal Rings Based on Symmetric Odd-Radix Number Systems.
Behrooz Parhami · Communications in Computing · 2005
An n-node network, with nodes numbered from – n/2 to n/2 – 1, is a chordal ring network with the chord lengths 1 = s0, s1, . . . , sk–1 (2 ≤ si < n/2) when each node i (– n/2 ≤ i < n/2) is connected to each of the 2k nodes i ± si mod n (0 ≤ i < k) via an undirected link, where “mod” represents symmetric residues. We study a class of chordal ring networks in which the chord length si is a power of an odd “radix” r, that is, si = r , for r ≥ 3. We show that this class of chordal rings, with their nodes indexed by radix-r numbers using the symmetric digit set [– (r – 1)/2, (r – 1)/2] are easy to analyze and offer a number of advantages in terms of static network parameters and dynamic performance in many application contexts.