Elsevier

Parallel Computing

Volume 21, Issue 8, August 1995, Pages 1327-1338
Parallel Computing

Short communication
Hyper-ring connection machines

https://doi.org/10.1016/0167-8191(95)00022-GGet rights and content

Abstract

A graph G = (V, E) is called a hyper-ring with N nodes (N-HR for short) if V = {0,…, N − 1} and E = {{u, v}¦v − u modulo N is a power of 2}. We study constructions, properties, spanners of HRs, and embeddings into HRs. A hypercube with N nodes, a grid of size a × b, and a complete binary tree with N nodes can be embedded as subgraphs into an N-HR. The stretch factors of three types of spanners given in this paper are at most [log2N], 2k − 1 for any 1 ≤ k ≤ [log2N], and 2k − 1 for any 2 ≤ k ≤ [log2N] − 1, respectively. The numbers of edges of these types of spanners are N − 1, at most N[(log2 N)k], and at most N[log2 N] − k)(2k) + Nk, respectively. Some of these spanners are superior in both stretch factors and numbers of edges to corresponding spanners for synchronizer γ of HRs.

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