Abstract
We first introduce a flexible interconnection network, called the hierarchical dual-net (HDN), with low node degree and short diameter for constructing a large-scale supercomputer. The HDN is constructed based on a symmetric product graph (base network). A k-level hierarchical dual-net, HDN(B,k,S), contains \({(2N_0)^{2^k}/(2\prod_{i=1}^{k}s_i)}\) nodes, where S = {s i |1 ≤ i ≤ k} is the set of integers with each s i representing the number of nodes in a super-node at the level i for 1 ≤ i ≤ k, and N 0 is the number of nodes in the base network B. The node degree of HDN(B,k,S) is d 0 + k, where d 0 is the node degree of the base network. The benefit of the HDN is that we can select suitable s i to control the growing speed of the number of nodes for constructing a supercomputer of the desired scale. Then we show that an HDN with the base network of p-ary q-cube is Hamiltonian and give an efficient algorithm for finding a Hamiltonian cycle in such hierarchical dual-nets.
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Li, Y., Peng, S., Chu, W. (2011). Finding a Hamiltonian Cycle in a Hierarchical Dual-Net with Base Network of p -Ary q -Cube. In: Xiang, Y., Cuzzocrea, A., Hobbs, M., Zhou, W. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2011. Lecture Notes in Computer Science, vol 7016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24650-0_11
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DOI: https://doi.org/10.1007/978-3-642-24650-0_11
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