28th Hawaii International Conference on System Sciences (HICSS'95) Hawaii, USA January 04-January 07 ISBN: 0-8186-6935-7
Gives a construction of embeddings of vertex-congestion 1 and dilation 4 of complete binary trees into star graphs. The height of the trees embedded into the n-dimensional star graph S/sub n/ is (n+1)[log/sub 2/ n]-2/sup [log n]+1/+1, which improves the previous result from Bouabdallah and Heydemann (1993, 1994) by more than n/2-1. We then construct embeddings of vertex-congestion 1, dilation at most (5n/4)+2, of complete binary trees into the n-dimensional star graph, whose height differs from the theoretical upper bound of log/sub 2/n! by less than 3[log/sub 2/n]. Our results show that the star networks can efficiently simulate algorithms that are intended for a binary tree architecture.
Index Terms:
trees (mathematics); multiprocessor interconnection networks; parallel architectures; complete binary tree embeddings; star graphs; vertex congestion; dilation; graph height; algorithm simulation; binary tree architecture
Citation:
M.-C. Heydemann, J. Opatrny, D. Sotteau, "Embeddings of complete binary trees into star graphs with congestion 1," hicss, pp.546, 28th Hawaii International Conference on System Sciences (HICSS'95), 1995 Usage of this product signifies your acceptance of the Terms of Use. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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