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2015•International Journal of Computer MathematicsRequires access

Linear layout of locally twisted cubes

Micheal Arockiaraj, Jessie Abraham, Jasintha Quadras, Arul Jeya Shalini

Open publisher page 13 citations

Abstract

The hypercube network is one of the most popular parallel computing networks since it has a simple structure and is easy to implement. The locally twisted cube is a newly introduced variant of the hypercube which has the same number of nodes and same number of connections per node as the hypercube, but has only half the diameter and better graph embedding capability as compared to hypercube. In this paper, we show that an n-dimensional locally twisted cube is constructed by forming a matching between the nodes of two disjoint copies of an (n−1)-dimensional hypercube. In addition, we embed the locally twisted cube into path with minimum layout.

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What this paper is about

The hypercube network is one of the most popular parallel computing networks since it has a simple structure and is easy to implement. The locally twisted cube is a newly introduced variant of the hypercube which has the same number of nodes and same number of connections per node as the hypercube, but has only half the diameter and better graph embedding capability as compared to hypercube. In this paper, we show that an n-dimensional locally twisted cube is constructed by forming a matching between the nodes of two disjoint copies of an (n−1)-dimensional hypercube. In addition, we embed the locally twisted cube into path with minimum layout.

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The hypercube network is one of the most popular parallel computing networks since it has a simple structure and is easy to implement. The locally twisted cube is a newly introduced variant of the hypercube which has the same number of nodes and same number of connections per node as the hypercube, but has only half the diameter and better graph embedding capability as compared to hypercube. In this paper, we show that an n-dimensional locally twisted cube is constructed by forming a matching between the nodes of two disjoint copies of an (n−1)-dimensional hypercube. In addition, we embed the locally twisted cube into path with minimum layout.

Key concepts: Hypercube, Cube (algebra), Embedding, Disjoint sets, Mathematics, Node (physics), Matching (statistics), Combinatorics

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