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A Class of Odd-Radix Chordal Ring Networks

An n-node network. with its nodes numbered from - Ln/2J to In/21- 1, is a chordal nng with chord lengths I = So < Si < ... < S1_1 < n/2 when an arbitrary node j (- Ln/2J <5. j < In/21) is connected to each of the 2k nodes j ± s, mod n (0 <5. i < k) via an undirected link, where "mod" represents (nearly) symmetric residues in [- Ln/2J, In121- I]. Vie study a class of chordal rings in which the chord length S, is a power of an odd "radix" r. that is, S, = rʹ, for r 0--0 20 + 1 2ʹ. 3. We show that this class of chordal rings, with their nodes indexed by radix-z integers using the symmetric digit set (-a, 0], are easy to analyze and offer a number of advantages in terms of static network parameters and dynamic performance for many application contexts. In particular, these networks allow a very simple optimal (shortest-path) routing algorithm that generates balanced traffic. We then briefly discuss fault tolerance properties of our networks and point out a number of variations and extensions to the basic structure.