Journal ArticleDOI
Connectivity of the crossed cube
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It was speculated that the connectivity of the n-dimensional crossed cube is n and this paper proves that the result is true.About:
This article is published in Information Processing Letters.The article was published on 1997-02-28. It has received 78 citations till now. The article focuses on the topics: Connectivity & Cube (algebra).read more
Citations
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Conditional diagnosability measures for large multiprocessor systems
TL;DR: A new measure of diagnosable, called conditional diagnosability, is introduced, by restricting that any faulty set cannot contain all the neighbors of any vertex in the graph, which shows the conditional Diagnosability of the n-dimensional hypercube to be 4(n - 2) +1, which is about four times as large as the classical diagnosis.
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The g-good-neighbor conditional diagnosability of hypercube under PMC model
TL;DR: The g -good-neighbor conditional diagnosability of Q n is several times larger than the classical diagnosable, and is proved to be 4( n − 2) + 1 under the PMC model.
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Diagnosability of crossed cubes under the comparison diagnosis model
TL;DR: It is shown that the n-dimensional crossed cube is n-diagnosable under a major diagnosis model-the comparison diagnosis model proposed by Malek and Maeng and Malek (1981) if n/spl ges/4; and the polynomial algorithm presented by Sengupta and Dahbura (1992) may be used to diagnose it.
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Edge congestion and topological properties of crossed cubes
TL;DR: It is shown that the edge congestion of crossed cubes is the same as that of hypercubes, and it is proved that wide diameter and fault diameter are [n/2]+2 and 2/sup n-1/ respectively.
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Optimal path embedding in crossed cubes
TL;DR: It is proved that paths of all lengths between [(n+1)/2] and 2/sup n/-1 can be embedded between any two distinct nodes with a dilation of 1 in the n-dimensional crossed cube.
References
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Journal ArticleDOI
Topological properties of hypercubes
Y. Saad,M.H. Schultz +1 more
TL;DR: The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing and propose a theoretical characterization of the n-cube as a graph.
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The crossed cube architecture for parallel computation
TL;DR: The construction of a crossed cube which has many of the properties of the hypercube, but has diameter only about half as large, is discussed, and it is shown that the CQ/sub n/ architecture can profitably emulate the ordinary hypercube.
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Embedding of tree networks into hypercubes
TL;DR: The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter but there are classes of graphs which can be embedded into a hypercube only with large expansion cost or large dilation cost.
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The twisted N-cube with application to multiprocessing
TL;DR: It is shown that by exchanging any two independent edges in any shortest cycle of the n-cube, its diameter decreases by one unit, which leads to the definition of a new class of n-regular graphs, denoted TQ/sub n/, with 2/sup n/ vertices and diameter n-1, which has the (n-1)-cube as subgraph.
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Embedding binary trees into crossed cubes
TL;DR: It is shown that the (2/sup n/-1) node complete binary tree can be embedded into the n-dimensional crossed cube with dilation 1.