### 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 |
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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 |

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### 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