### Abstract

Distributed loop networks are networks with at least one ring structure. They are widely used in the design of local area networks, multimodule memory organizations, data alignments in parallel memory systems, and supercomputer architecture. In this paper, we give a systematic and unified method of solutions in the design and implementation of these networks. We show that doubly linked loop networks with transmission delay less than or equal to (1+ε)√3N can be constructed asymptotically for sufficiently large N, the number of nodes in the network. This is close to the optimal value within a number which is small as compared to N. We then give several infinite classes of values of N for which optimal doubly linked loop networks can be actually designed. The method is then generalized to obtain a new upper bound for possible transmission delays in multiply linked loop networks. Routing and rerouting algorithms are designed for the optimal loop networks.

Original language | English |
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Pages (from-to) | 223-241 |

Number of pages | 19 |

Journal | Theoretical Computer Science |

Volume | 100 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 22 1992 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Theoretical Computer Science*,

*100*(1), 223-241. https://doi.org/10.1016/0304-3975(92)90370-U

**Distributed loop network with minimum transmission delay.** / Erdős, P.; Hsu, D. Frank.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 100, no. 1, pp. 223-241. https://doi.org/10.1016/0304-3975(92)90370-U

}

TY - JOUR

T1 - Distributed loop network with minimum transmission delay

AU - Erdős, P.

AU - Hsu, D. Frank

PY - 1992/6/22

Y1 - 1992/6/22

N2 - Distributed loop networks are networks with at least one ring structure. They are widely used in the design of local area networks, multimodule memory organizations, data alignments in parallel memory systems, and supercomputer architecture. In this paper, we give a systematic and unified method of solutions in the design and implementation of these networks. We show that doubly linked loop networks with transmission delay less than or equal to (1+ε)√3N can be constructed asymptotically for sufficiently large N, the number of nodes in the network. This is close to the optimal value within a number which is small as compared to N. We then give several infinite classes of values of N for which optimal doubly linked loop networks can be actually designed. The method is then generalized to obtain a new upper bound for possible transmission delays in multiply linked loop networks. Routing and rerouting algorithms are designed for the optimal loop networks.

AB - Distributed loop networks are networks with at least one ring structure. They are widely used in the design of local area networks, multimodule memory organizations, data alignments in parallel memory systems, and supercomputer architecture. In this paper, we give a systematic and unified method of solutions in the design and implementation of these networks. We show that doubly linked loop networks with transmission delay less than or equal to (1+ε)√3N can be constructed asymptotically for sufficiently large N, the number of nodes in the network. This is close to the optimal value within a number which is small as compared to N. We then give several infinite classes of values of N for which optimal doubly linked loop networks can be actually designed. The method is then generalized to obtain a new upper bound for possible transmission delays in multiply linked loop networks. Routing and rerouting algorithms are designed for the optimal loop networks.

UR - http://www.scopus.com/inward/record.url?scp=0026879912&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026879912&partnerID=8YFLogxK

U2 - 10.1016/0304-3975(92)90370-U

DO - 10.1016/0304-3975(92)90370-U

M3 - Article

AN - SCOPUS:0026879912

VL - 100

SP - 223

EP - 241

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1

ER -