A new family of extremal interconnection networks

© World Scientific Publishing CompanyWe extensively discuss a new interconnection network topology, denoted by ϒ(n,r). Firstly, the ϒ(n, 2) network is shown to provide average cost 3log[sub 2] n while providing superior fault tolerance characteristics. It is defined over any natural number of nodes n using 2n - 3 edges for an average degree of 4 and has diameter no greater than k = [log[sub 2] n] with average diameter as small as &kmacr; = ½ The network is planar and has cyclomatic num- ber n - 2. For n = 2[sup t] the unbounded maximum degree is 2 log[sub 2] n - 1 believed indicative of generally a maximum unbounded degree O(log[sub 2] n). The bisection width ranges from 3 when n = 2[sup t] to t + 1 when n = 2[sup t] + 1. Secondly, we provide the ϒ[sup *](n, r) network of bounded degree 2r. For n -- r[sup t] the ϒ[sup *] (n, r) network has asymptotically better average cost than the general deBruijn(r, t) network while also maintaining planarity and cyclomatic property of ϒ(n, 2). The ϒ family exhibits unique extremal properties of both theoretical interest and practical importance.Aaron Harwood and Hong She