### Abstract

In this paper, a new algorithm based on hierarchical aggregation/disaggregation and decomposition/composition (HAD) scheme is proposed to solve the optimal routing problems (ORP) for hierarchically structured networks of multi-layer backbones. Our algorithm has two major differences with the existing HAD algorithms for hierarchically clustered networks [1], [2]: 1) our algorithm works with more general networks than the networks with the clustered structure; 2) our algorithm parallelizes the computations for different commodities (message flows defined by a pair of origin node and destination node) so that it speeds up with a parallel time complexity of O(mlog^{2}(n)), which is much less than O(Mlog^{2}(n)) needed for the existing HAD algorithms. Here, n is the number of nodes in the network; M is the number of commodities and m is a positive number usually much smaller than M and is a function of the patterns of all the commodities including the locations of all origin nodes and destination nodes, and the flow demand of each commodity. Furthermore, our algorithm can make a trade-off between the run time and the optimality, i.e., by allowing the solution to be sub-optimal, our algorithm can save great amount of computation time. The implementation of the algorithm for a 200-node network is simulated using OPNET simulation package (OPNET or Optimized Network Engineering Tools is developed by MIL3, Inc.), and the test results are consistent with our analysis.

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

Pages (from-to) | 939-953 |

Number of pages | 15 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 7 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1 Dec 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Data network
- Distributed computation
- Gradient projection method
- Hierarchically structured network
- Optimal routing
- Parallel processing

### ASJC Scopus subject areas

- Signal Processing
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

**A new HAD algorithm for optimal routing of hierarchically structured data networks.** / Huang, Garng Morton; Zhu, Shan.

Research output: Contribution to journal › Article

*IEEE Transactions on Parallel and Distributed Systems*, vol. 7, no. 9, pp. 939-953. https://doi.org/10.1109/71.536938

}

TY - JOUR

T1 - A new HAD algorithm for optimal routing of hierarchically structured data networks

AU - Huang, Garng Morton

AU - Zhu, Shan

PY - 1996/12/1

Y1 - 1996/12/1

N2 - In this paper, a new algorithm based on hierarchical aggregation/disaggregation and decomposition/composition (HAD) scheme is proposed to solve the optimal routing problems (ORP) for hierarchically structured networks of multi-layer backbones. Our algorithm has two major differences with the existing HAD algorithms for hierarchically clustered networks [1], [2]: 1) our algorithm works with more general networks than the networks with the clustered structure; 2) our algorithm parallelizes the computations for different commodities (message flows defined by a pair of origin node and destination node) so that it speeds up with a parallel time complexity of O(mlog2(n)), which is much less than O(Mlog2(n)) needed for the existing HAD algorithms. Here, n is the number of nodes in the network; M is the number of commodities and m is a positive number usually much smaller than M and is a function of the patterns of all the commodities including the locations of all origin nodes and destination nodes, and the flow demand of each commodity. Furthermore, our algorithm can make a trade-off between the run time and the optimality, i.e., by allowing the solution to be sub-optimal, our algorithm can save great amount of computation time. The implementation of the algorithm for a 200-node network is simulated using OPNET simulation package (OPNET or Optimized Network Engineering Tools is developed by MIL3, Inc.), and the test results are consistent with our analysis.

AB - In this paper, a new algorithm based on hierarchical aggregation/disaggregation and decomposition/composition (HAD) scheme is proposed to solve the optimal routing problems (ORP) for hierarchically structured networks of multi-layer backbones. Our algorithm has two major differences with the existing HAD algorithms for hierarchically clustered networks [1], [2]: 1) our algorithm works with more general networks than the networks with the clustered structure; 2) our algorithm parallelizes the computations for different commodities (message flows defined by a pair of origin node and destination node) so that it speeds up with a parallel time complexity of O(mlog2(n)), which is much less than O(Mlog2(n)) needed for the existing HAD algorithms. Here, n is the number of nodes in the network; M is the number of commodities and m is a positive number usually much smaller than M and is a function of the patterns of all the commodities including the locations of all origin nodes and destination nodes, and the flow demand of each commodity. Furthermore, our algorithm can make a trade-off between the run time and the optimality, i.e., by allowing the solution to be sub-optimal, our algorithm can save great amount of computation time. The implementation of the algorithm for a 200-node network is simulated using OPNET simulation package (OPNET or Optimized Network Engineering Tools is developed by MIL3, Inc.), and the test results are consistent with our analysis.

KW - Data network

KW - Distributed computation

KW - Gradient projection method

KW - Hierarchically structured network

KW - Optimal routing

KW - Parallel processing

UR - http://www.scopus.com/inward/record.url?scp=0030247085&partnerID=8YFLogxK

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U2 - 10.1109/71.536938

DO - 10.1109/71.536938

M3 - Article

VL - 7

SP - 939

EP - 953

JO - IEEE Transactions on Parallel and Distributed Systems

JF - IEEE Transactions on Parallel and Distributed Systems

SN - 1045-9219

IS - 9

ER -