High Performance Computing and Grid in Asia Pacific Region, International Conference on (2005)
Nov. 30, 2005 to Dec. 3, 2005
Jywe-Fei Fang , National Taichung University, Taichung, Taiwan
Kuan-Chou Lai , National Taichung University, Taichung, Taiwan
Ching-Chi Kao , St. John's University, Taipei, Taiwan
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.
K. Lai, C. Kao and J. Fang, "The Linear Layout of the Incomplete Hypercube," High Performance Computing and Grid in Asia Pacific Region, International Conference on(HPCASIA), Beijing, China, 2005, pp. 61-66.