### Abstract

We study the cross product as a method for generating and analyzing interconnection network topologies for multiprocessor systems. Consider two interconnection graphs G_{1} and G_{2} each with some established properties such as symmetry, low degree and diameter, scalability, simple optimal routing, recursive structure (partitionability), fault tolerance, existence of node-disjoint paths, low cost embedding, and efficient broadcasting. We investigate and evaluate the corresponding properties for the cross product of G_{1} and G_{2} based on the properties of G_{1} and those of G_{2}. We also give a mathematical characterization of product families of graphs which are closed under the cross product operation. This investigation is useful in two ways. On one hand, it gives a new tool for further studying some of the known interconnection topologies, such as the hypercube and the mesh, which can be defined using the cross product operation. On the other hand, it can be used in defining and evaluating new interconnection graphs using the cross product operation on known topologies.

Original language | English |
---|---|

Pages (from-to) | 109-118 |

Number of pages | 10 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 8 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1997 |

### Fingerprint

### Keywords

- Broadcasting
- Embedding
- Interconnection networks
- Parallel paths
- Product networks
- Routing

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*8*(2), 109-118. https://doi.org/10.1109/71.577251

**The cross product of interconnection networks.** / Day, Khaled; Ai-Ayyoub, Abdel Elah.

Research output: Contribution to journal › Article

*IEEE Transactions on Parallel and Distributed Systems*, vol. 8, no. 2, pp. 109-118. https://doi.org/10.1109/71.577251

}

TY - JOUR

T1 - The cross product of interconnection networks

AU - Day, Khaled

AU - Ai-Ayyoub, Abdel Elah

PY - 1997

Y1 - 1997

N2 - We study the cross product as a method for generating and analyzing interconnection network topologies for multiprocessor systems. Consider two interconnection graphs G1 and G2 each with some established properties such as symmetry, low degree and diameter, scalability, simple optimal routing, recursive structure (partitionability), fault tolerance, existence of node-disjoint paths, low cost embedding, and efficient broadcasting. We investigate and evaluate the corresponding properties for the cross product of G1 and G2 based on the properties of G1 and those of G2. We also give a mathematical characterization of product families of graphs which are closed under the cross product operation. This investigation is useful in two ways. On one hand, it gives a new tool for further studying some of the known interconnection topologies, such as the hypercube and the mesh, which can be defined using the cross product operation. On the other hand, it can be used in defining and evaluating new interconnection graphs using the cross product operation on known topologies.

AB - We study the cross product as a method for generating and analyzing interconnection network topologies for multiprocessor systems. Consider two interconnection graphs G1 and G2 each with some established properties such as symmetry, low degree and diameter, scalability, simple optimal routing, recursive structure (partitionability), fault tolerance, existence of node-disjoint paths, low cost embedding, and efficient broadcasting. We investigate and evaluate the corresponding properties for the cross product of G1 and G2 based on the properties of G1 and those of G2. We also give a mathematical characterization of product families of graphs which are closed under the cross product operation. This investigation is useful in two ways. On one hand, it gives a new tool for further studying some of the known interconnection topologies, such as the hypercube and the mesh, which can be defined using the cross product operation. On the other hand, it can be used in defining and evaluating new interconnection graphs using the cross product operation on known topologies.

KW - Broadcasting

KW - Embedding

KW - Interconnection networks

KW - Parallel paths

KW - Product networks

KW - Routing

UR - http://www.scopus.com/inward/record.url?scp=0031076525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031076525&partnerID=8YFLogxK

U2 - 10.1109/71.577251

DO - 10.1109/71.577251

M3 - Article

AN - SCOPUS:0031076525

VL - 8

SP - 109

EP - 118

JO - IEEE Transactions on Parallel and Distributed Systems

JF - IEEE Transactions on Parallel and Distributed Systems

SN - 1045-9219

IS - 2

ER -