منابع مشابه
Embedding of Hypercubes into Grids
We consider one-to-one embeddings of the n-dimensional hypercube into grids with 2n vertices and present lower and upper bounds and asymptotic estimates for minimal dilation, edge-congestion, and their mean values. We also introduce and study two new cost-measures for such embeddings, namely the sum over i = 1, ..., n of dilations and the sum of edge congestions caused by the hypercube edges of...
متن کاملEmbedding 3-dimensional Grids into Optimal Hypercubes
The hypercube is a particularly versatile network for parallel computing. It is well-known that 2-dimensional grid machines can be simulated on a hypercube with a small constant communication overhead. We introduce new easily computable functions which embed many 3-dimensional grids into their optimal hypercubes with dilation 2. Moreover, we show that one can reduce the open problem to recogniz...
متن کاملEmbedding multidimensional grids into optimal hypercubes
Let G and H be graphs, with |V (H)| ≥ |V (G)|, and f : V (G) → V (H) a one to one map of their vertices. Let dilation(f) = max{distH(f(x), f(y)) : xy ∈ E(G)}, where distH(v, w) is the distance between vertices v and w of H. Now let B(G,H) = minf{dilation(f)}, over all such maps f . The parameter B(G,H) is a generalization of the classic and well studied “bandwidth” of G, defined as B(G,P (n)), ...
متن کاملDilation-5 Embedding of 3-Dimensional Grids into Hypercubes
W e present an algorithm t o map the nodes of a 3. dimensional grid t o the nodes of i ts optimal hypercube on a one-to-one basis wi th dilation at most 5.
متن کاملEmbedding hyperpyramids into hypercubes
A &k, d ) hyperpyramid is a level structure of k hypercubes, where the hypercube at level i is of dimension id, and a node at level i 1 is connected to every node in a &dimensional subcube at level i, except for the leaf level k. Hyperpyramids contain pyramids as propy subgraphs. We show that a hyperpyramid P(k, d ) can be embedded in a hypercube with minimal expansion and dilation = d. The con...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1992
ISSN: 0022-0000
DOI: 10.1016/0022-0000(92)90030-m