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Linear Layout of the Supercube Jywe-Fei FANG Publication IEICE TRANSACTIONS on Information and Systems Vol.E89-D No.2 pp.779-782 Publication Date: 2006/02/01 Online ISSN: 1745-1361 DOI: 10.1093/ietisy/e89-d.2.779 Print ISSN: 0916-8532 Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science) Category: Network Keyword: interconnection networks, supercubes, layout, embedding in books, Full Text: PDF(179.3KB)>>
Summary: In this paper, we study the layout problem of the supercube by embedding-in-book technique. The supercube, a generalization of the hypercube, can be constructed for an arbitrary system size. Moreover, it has the same diameter and connectivity of the corresponding hypercube. Embedding a graph in book is to place nodes along the spine of the book and to draw the edges such that edges residing in a page do not cross. An n-dimensional hypercube is regular because the degree of each node is n. The corresponding supercube with N nodes, where 2n-1 < N  2n and N ≠ 3 2n-2, is irregular because the degree of each node ranges from 2n - 2 to n - 1. Although Chung et al. have shown that an n-dimensional hypercube can be embedded with n - 1 pages, to lay out the supercube remains a challenging problem owing to its higher degree and irregular structure. In this paper, we show that a supercube of N nodes, where 2n-1 < N 2n, can also be embedded with n - 1 pages and book width N - 2n-2 for 2n-1 < N < 32n-2, and 2n-1 for 32n-2 N 2n. | ||||||||||
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