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Embedding an Arbitrary Binary Tree into the Star Graph
April 1996 (vol. 45 no. 4)
pp. 475-481

Abstract—Binary tree structures have been very useful in solving divide-and-conquer type of problems. Embedding binary trees into another network—the host network—helps in designing solutions for the host network using the known solutions on binary trees. Embedding arbitrary binary trees into networks, in particular into the hypercube, has been addressed in the literature. The latter was achieved with load 1 and constant dilation.

The n-star graph is a recently introduced interconnection network for massively parallel systems. It enjoys symmetry and fault tolerance properties that make it a viable alternative to the hypercube. In this paper, we address the problem of embedding arbitrary binary trees into the n-star graph. This work is the first to present such an embedding. The tree has $\lfloor e(n - 1)!\rfloor$ or fewer vertices. The embedding leads to load 1 and constant dilation for all values of n. It therefore enables the star graph to efficiently simulate an arbitrary binary tree with only a constant factor of communication delay.

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Index Terms:
Star graph, interconnection network, massively parallel, binary tree, embedding, load, dilation, tree partitioning.
Nader Bagherzadeh, Martin Dowd, Nayla Nassif, "Embedding an Arbitrary Binary Tree into the Star Graph," IEEE Transactions on Computers, vol. 45, no. 4, pp. 475-481, April 1996, doi:10.1109/12.494105
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