Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
IEEE Transactions on Computers
Topological Properties of Hypercubes
IEEE Transactions on Computers
The design and analysis of parallel algorithms
The design and analysis of parallel algorithms
Embedding planar graphs in four pages
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Structural and Tree Embedding Aspects of Incomplete Hypercubes
IEEE Transactions on Computers
An effective routing algorithm in incomplete hypercubes
Parallel Computing
Optimum embedding of complete graphs in books
Discrete Mathematics - Special issue on Graph theory
Efficient generation of the binary reflected gray code and its applications
Communications of the ACM
| Hi-index | 0.00 |
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.