Hyper-Ring Connection Machines

A graph G = (V,E) is called a hyper-ring with N nodes (N-HR for short) if V = {O,...,N 1) and E = {{u,u}1u U modulo N is a power of 2). We study constructions and spanners of HRs, and embeddings into HRs. The stretch factors of three types of spanners given in this paper are at most [log, q, 2k1 for any 15 k 5 rlog,N], and 2k1 for any 0 5 k 5 [log, N] 1, respectively. The numbers of edges of these types of spanners are N 1, at most N[(log, N ) / k ] and at most N(rlog, N]-k)/(2k)+Nk, respectively. Some of these spanners are superior in both stretch factors and numbers of edges to corresponding spanners for syflchronirer y of HRs.