@inproceedings{d5b243d5a56941e38e620653e4d9deb7,
title = "Efficient embeddings into the hypercube using matrix transformations",
abstract = "The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. Through such embeddings the algorithms originally developed for one architecture can be directly mapped to another architecture. This paper describes novel methods, based on matrix transformations, for efficiently embedding different networks into the hypercube (binary n-cube). First, we use this method to embed r-ary m-cubes into a binary n-cube of the same size with dilation 1. While our method has the same dilation as traditional methods using reflected Gray code, it has the additional property of making the layout of the binary n-cube more suitable for divide-and-conquer algorithms. Second, we use our matrix transformation method to optimally embed hierarchical interconnection networks into the binary n-cube which we would not achieve using reflected Gray code embedding. Thus, this embedding method has significant practical importance in enhancing the capabilities of the hypercube.",
keywords = "Dilation, Embedding, Hierarchical networks, Hypercube, R-ary m-cube",
author = "Mounir Hamdi and Song, {S. W.}",
note = "Publisher Copyright: {\textcopyright} 1995 ACM.; 9th International Conference on Supercomputing, ICS 1995 ; Conference date: 03-07-1995 Through 07-07-1995",
year = "1995",
month = jul,
day = "3",
doi = "10.1145/224538.224572",
language = "English",
series = "Proceedings of the International Conference on Supercomputing",
publisher = "Association for Computing Machinery",
pages = "280--288",
booktitle = "Proceedings of the 9th International Conference on Supercomputing, ICS 1995",
address = "United States",
}