Optimal embeddings in the Hamming cube networks

Abstract

This paper studies network embeddings in the Hamming cubes, a recently designed interconnection topology for multicomputers. The Hamming cube networks are supergraphs of incomplete hypercubes such that the additional edges form an extra binomial spanning tree. The recursively constructible and unit incremental Hamming cubes have better properties than hypercubes, including half of logarithmic diameter and higher fault-tolerance. They also support simple routing and efficient broadcasting schemes. In this paper, we show that Hamiltonian paths and cycles of all lengths, complete binary trees and their several variants are subgraphs of Hamming cubes. Our embeddings have both dilation and expansion equal to one. Furthermore, taking advantage of the enhanced edges in the Hamming cubes, tree machines can be embedded with dilation of one and expansion of 7/6. Thus, Hamming cubes provide embeddings at a lower cost than (incomplete) hypercubes of the same size.KeywordsNetwork embeddingdilationinterconnection networkHamming cubeincomplete hypercubebinary treehypertreetree machine