High Performance Computing and Grid in Asia Pacific Region, International Conference on (2005)

Beijing, China

Nov. 30, 2005 to Dec. 3, 2005

ISBN: 0-7695-2486-9

pp: 61-66

Kuan-Chou Lai , National Taichung University, Taichung, Taiwan

Ching-Chi Kao , St. John's University, Taipei, Taiwan

Jywe-Fei Fang , National Taichung University, Taichung, Taiwan

ABSTRACT

In this paper, we study the linear layout problem of an incomplete hypercube by the embedding-in-book technique. An incomplete hypercube is a generalization of the hypercube in the sense that the number of nodes can be an arbitrary number. Embedding a graph in a book is to place nodes on the spine of a book and to draw the edges such that edges residing in a page do not cross. In this paper, we propose a scheme to embed an incomplete hypercube of 2^n+2^m nodes, where n \ge m \ge 0, with n-1 pages, cumulative page width 2n+2m-3; and book width 2^n-1+2^m-1 for n \ge m \ge 0, 2^n-1 for n \ge m = 0. Moreover, this scheme can be applied to an arbitrary size of an incomplete hypercube.

INDEX TERMS

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CITATION

Kuan-Chou Lai,
Ching-Chi Kao,
Jywe-Fei Fang,
"The Linear Layout of the Incomplete Hypercube",

*High Performance Computing and Grid in Asia Pacific Region, International Conference on*, vol. 00, no. , pp. 61-66, 2005, doi:10.1109/HPCASIA.2005.93