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<p><b>Abstract</b>—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 [<ref rid="bibl09391" type="bib">1</ref>], [<ref rid="bibl09392" type="bib">2</ref>]: 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 <it>O</it>(<it>m</it>log<super>2</super>(<it>n</it>)), which is much less than <it>O</it>(<it>M</it>log<super>2</super>(<it>n</it>)) needed for the existing HAD algorithms. Here, <it>n</it> is the number of nodes in the network; <it>M</it> is the number of commodities and <it>m</it> is a positive number usually much smaller than <it>M</it> 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 <it>OPNET</it> simulation package (OPNET or Optimized Network Engineering Tools is developed by MIL3, Inc.), and the test results are consistent with our analysis.</p>
Optimal routing, parallel processing, distributed computation, data network, gradient projection method, hierarchically structured network.

G. M. Huang and S. Zhu, "A New HAD Algorithm for Optimal Routing of Hierarchically Structured Data Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 7, no. , pp. 939-953, 1996.
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