New graph model and its routing algorithm for rearrangeable networks
This paper introduces a new simple graphical representation, called an N-leaf Dual Complete Binary Tree (N-leaf DCB-tree), for (2 log2N−1)-stage networks. The N-leaf DCB-tree representation method has hierarchical and recursive characteristics. Due to the hierarchical property, it provides an analytical and systematic model for a multistage interconnection network with respect to a permutation realizability. Based on the recursive property of DCB-tree structure, we present a universal necessary and sufficient condition of a conflict-free connection pattern for N one-to-one simultaneous connection paths in multistage interconnection networks. Depending on the class of a given (2 log2N−1)-stage network, this universal condition can be changed. Also this N-leaf DCB-tree model is shown to be very useful in comparing the permutation capabilities of various network topologies. The N-leaf DCB-tree model can convert a routing problem to a conflict-free assignment problem for N binary numbers where each binary number is a (log2N−1)-bit string. Converting to a conflict-free assignment problem may make it easier to attack the rearrangeablity of a (2 log2N−1)-stage network in a class of Shuffle-Exchange equivalent netwrks (E- class).
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