Abstract
In this paper, we characterize a class of graphs which can be embedded on a boolean cube. Some of the graphs in this class are identified with the well known graphs such asmulti-dimensional mesh of trees, tree of meshes, etc. We suggest (i) an embedding of anr-dimensional mesh of trees ofn r(r+1)−rn r−1 nodes on a boolean cube of (2n)r nodes, and (ii) an embedding of a tree of meshes with 2n 2 logn+n 2 nodes on a boolean cube withn 2 exp2 (log (2 logn+1)]) nodes.
Similar content being viewed by others
References
S. N. Bhatt and I. C. F. Ipsen,How to embed trees in hypercubes, Tech. Rep. YALEU/CSD/RR-443, Department of Computer Science, Yale University, Dec. 1985.
S. Bhatt, F. T. Leighton and A. Rosenberg,Optimal simulation of tree machines, in Proc. 27th Annu. IEEE Symp. Found. Comp. Sci., pp. 264–282, 1986.
M. Y. Chan and F. Y. L. Chin,On embedding rectangular grids in hypercube, IEEE Trans. Computers, vol. 37, No. 10, Oct. 1988.
Jia-Wei Hong, Kurt Mehlhorn and Arnold L. Rosenberg,Cost trade-offs in graph embeddings, with applications, Journal of the Association of Computing Machinery, Vol. 30, No. 4, pp. 709–728, Oct. 1983
S. L. Johnson,Communication efficient basic linear algebra computation on hypercube architecture, Journal of Parallel and Distributed Computing, vol. 4 pp. 133–172, 1987.
D. W. Krumme, K. N. Venkataraman, and G. Cybenko,Hypercube embedding is NP-complete, in First Hypercube Conference, M. Heath, editor, pages 148–157, SIAM, Knoxville, Tennessee, August 1985.
F. T. Leighton,New lower bound techniques for VLSI, in Proc. 22nd Annu. IEEE Symp. foundation com. sci., pp. 1–12, October 1981.
F. T. Leighton,Private communication, 1989.
R. Miller and Q. F. Stout,Some graph and image processing algorithms for hypercube, in Hypercube Multiprocessors 1987, Philadelphia, PA: SIAM, pp. 418–425, 1987.
R. Miller and Q. F. Stout,Efficient parallel convex hull algorithm, IEEE Trans. on Computers, Vol 37, No. 12, pp. 1605–1618, December 1988.
R. Miller and Q. F. Stout,Simulating essential pyramids, IEEE Trans. on Computers, Vol. 37, No. 12, pp. 1642–1647, December 1988.
D. Nath, S. N. Maheshwari and P. C. P. Bhatt,Efficient VLSI networks for parallel processing based on orthogonal trees, IEEE Trans. Comput., Vol. C-32, No. 6, pp. 569–581, June 1983.
Y. Saad and M. H. Schultz,Topological properties of hypercubes, IEEE Trans. on Computers, Vol. 37, Number 7, pp. 867–872, 1988.
David S. Scott and Joe Brandenburg,Minimal mesh embedding in binary hypercubes, IEEE Trans. Computers, vol. 37, No. 10, pp. 1284–1285, October 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zubair, M., Gupta, S.N. Embeddings on a boolean cube. BIT 30, 245–256 (1990). https://doi.org/10.1007/BF02017346
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02017346