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Finding a hamiltonian cycle in a hierarchical dual-net with base network of p -ary q -cube
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ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
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In this paper, we propose a new universal network, called recursive dual-net (RDN), as a potential candidate for the interconnection network of supercomputers with very large scale. The recursive dual-net is based on a recursive dual-construction of a base network. A k -level dual-construction for k 0 creates a network containing $(2m)^{2^k}/2$ nodes with node-degree d + k , where m and d are the number of nodes and the node-degree, respectively, of the base network. The recursive dual-net is node and edge symmetric and can contain huge number of nodes with small node-degree and short diameter. For example, we can construct a symmetric RDN connecting more than 3-million nodes with only 6 links per node and a diameter of 22. We investigate the topological properties of the recursive dual-net and compare it to that of other networks including 3D torus, WK-recursive network, hypercube, cube-connected-cycle, and dual-cube. We also establish the basic routing and broadcasting algorithms for the proposed recursive dual-net.