Squashed embedding of E-R schemas in hypercubes

We have been investigating an approach to parallel database processing based on treating Entity-Relationship (E-R) schema graphs as dataflow graphs. A prerequisite is to find appropriate embeddings of the schema graphs into a processor graph, in this case a hypercube. This paper studies a class of adjacency preserving embeddings that map a node in the schema graph into a subcube (relaxed squashed or RS embeddings) or into adjacent subcubes (relaxed extended squashed or RES embeddings) of a hypercube. The mapping algorithm is motivated by the technique used for state assignment in asynchronous sequential machines. In general, the dimension of the cube required for squashed embedding of a graph is called the weak cubical dimension or WCD of the graph. The RES embedding provides an RES-WCD of O([left ceiling]log2n[right ceiling]) for a completely connected graph, Kn, and RS embedding provides an RS-WCD of O([left ceiling]log2n[right ceiling] + [left ceiling]log2m[right ceiling]) for a completely connected bigraph, Km,n. Typical E-R graphs are incompletely connected bigraphs. An algorithm for embedding incomplete bigraphs is presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28651/1/0000467.pd

Special issue on algorithms for hypercube computers : Guest editor's introduction

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28649/1/0000465.pd

Some Theoretical Results of Hypercube for Parallel Architecture

This paper surveys some theoretical results of the hypercube for design of VLSI architecture. The parallel computer including the hypercube multiprocessor will become a leading technology that supports efficient computation for large uncertain systems