• Journal of KIISE:Computer Systems and Theory
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• v.36 no.3
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• pp.149-157
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• 2009

The crossed cube, a variation of the hypercube, possesses a better topological property than the hypercube in its diameter that is about half of that of the hypercube. It has been known that an N-node complete binary tree is a subgraph of an (N+1)-node crossed cube [P. Kulasinghe and S. Bettayeb, 1995]. However, efficient embedding methods have not been known for the case that the number of nodes of the complete binary tree is greater than that of the crossed cube. In this paper, we show that an N-node complete binary tree can be embedded into an M-node crossed cube with dilation 1 and load factor [N/M], N>M$\geq$2. The dilation and load factor is optimal. Our embedding has a property that the tree nodes on the same level are evenly distributed over the crossed cube nodes. The property is especially useful when tree-structured algorithms are processed on a crossed cube in a level-by-level way.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.5
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• pp.335-343
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• 2009

The crossed cube has received great attention because it has equal or superior properties compared to the hypercube that is widely known as a versatile parallel processing system. It has been known that disjoint two copies of a mesh of size $4{\times}2^m$ or disjoint four copies of a mesh of size $8{\times}2^m$ can be embedded into a crossed cube with dilation 1 and expansion 1 [Dong, Yang, Zhao, and Tang, 2008]. However, it is not known that disjoint multiple copies of a mesh with more than eight rows and columns can be embedded into a crossed cube with dilation 1 and expansion 1. In this paper, we show that disjoint $2^{n-1}$ copies of a mesh of size $2^n{\times}2^m$ can be embedded into a crossed cube with dilation 1 and expansion 1 where $n{\geq}1$ and $m{\geq}3$. Our result is optimal in terms of dilation and expansion that are important measures of graph embedding. In addition, our result is practically usable in allocating multiple jobs of mesh structure on a parallel computer of crossed cube structure.

• The KIPS Transactions:PartA
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• v.15A no.6
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• pp.301-308
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• 2008

The crossed cube has received great attention because it has equal or superior properties to the hypercube that is widely known as a versatile parallel processing system. It has been known that a mesh of size $2{\times}2^m$ can be embedded into a crossed cube with dilation 1 and expansion 1 and a mesh of size $4{\times}2^m$ with dilation 1 and expansion 2. However, as we know, it has been a conjecture that a mesh with more than eight rows and columns can be embedded into a crossed cube with dilation 1. In this paper, we show that a mesh of size $2^n{\times}2^m$ can be embedded into a crossed cube with dilation 1 and expansion $2^{n-1}$ where $n{\geq}1$ and $m{\geq}3$.

• The KIPS Transactions:PartA
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• v.18A no.6
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• pp.225-232
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• 2011

Restricted Hypercube-Like (RHL) graphs are a graph class that widely includes useful interconnection networks such as crossed cube, Mobius cube, Mcube, twisted cube, locally twisted cube, multiply twisted cube, and generalized twisted cube. In this paper, we show that for an m-dimensional RHL graph G, $m{\geq}4$, with an arbitrary faulty edge set $F{\subset}E(G)$, ${\mid}F{\mid}{\leq}m-2$, graph $G{\setminus}F$ has a hamiltonian path between any distinct two nodes s and t if dist(s, V(F))${\neq}1$ or dist(t, V(F))${\neq}1$. Graph $G{\setminus}F$ is the graph G whose faulty edges are removed. Set V(F) is the end vertex set of the edges in F and dist(v, V(F)) is the minimum distance between vertex v and the vertices in V(F).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.6
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• pp.1463-1469
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• 1996

A crossed incoplete hypercube structure is based on previous crossed hypercube structure that reduces the diameter about 50% and has the same complexity with general hypercube and is able to expand to any number of nodes. In this study, we proposed a fault-tolerant adaptive routing scheme and broadcasting scheme. Fault-tolerant adaptive routing scheme is resilient to system faults. And performance evaluation is executed on the proposed sturcture. It is enhanced about 30%.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.2
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• pp.427-434
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• 1996

Hypercube has some advantages such as small diameter between nodes and relatively simple routing scheme, so it is one of the most popular interconnection networks used in real systems. But to make this structure more practical, it is required to reduce its diameter and to be able to expand it to any number of nodes. In this study, we proposed a Crossed Incomplete Hypercube structure. This scheme is based on the previous Crossed Hypercube topology that reduces the diameter about 50% and has the same complexity with general hypercube and is able to expand to any number of nodes. We also proposed a fixed routing scheme for this structure. In the repect of the average path and the average routing time, this structure shows an enhanced performance about 30% and it is enhanced about 20% ifn the average traffic density.