Embedding of tree networks into hypercubes

Journal Article · Thu Aug 01 00:00:00 EDT 1985 · J. Parallel Distrib. Comput.; (United States)

DOI:https://doi.org/10.1016/0743-7315(85)90026-7· OSTI ID:6777908

Wu, A Y

The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter. Graphs such as trees and arrays can be embedded into a hypercube with small costs. The design of the embedding mappings makes use of the structures of these graphs. In general, there is a trade-off between the dilation cost and the expansion cost. Rosenberg illustrates how one of these costs can be minimized only at the expense of a dramatic increase in the other cost in three situations where binary trees are the host graphs. This paper shows that there is no embedding of a complete binary tree into a hypercube with dilation cost of 1 and expansion cost less than 2. But there is an embedding with dilation cost 1 and expansion cost approximately 2, and there is an embedding with dilation cost 2 and expansion cost approximately 1. For embedding of general graphs, if the size of the hypercube is minimal, then the dilation cost of the embedding may be as large as log (number of nodes in the graph). On the other hand, there is always an embedding of an n node graph into a degree n - 1 hypercube (very high expansion cost) with a dilation cost of 2. We have also shown that there are classes of graphs which cannot have adjacency-preserving (dilation cost = 1) embeddings into hypercubes of any size.

• Research Organization: Dept. of Mathematics, Statistics and Computer Science, The American Univ., Washington, DC 20016
• OSTI ID: 6777908
• Journal Information: J. Parallel Distrib. Comput.; (United States), Vol. 2:3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
PARALLEL PROCESSING
GRAPHS
SUPERCOMPUTERS
ALGORITHMS
ARRAY PROCESSORS
COMPUTER ARCHITECTURE
COMPUTER GRAPHICS
COST
DEGREES OF FREEDOM
COMPUTERS
DIGITAL COMPUTERS
MATHEMATICAL LOGIC
PROGRAMMING
990210* - Supercomputers- (1987-1989)