Discussiones Mathematicae Graph Theory 28(3) (2008) 463-476
doi: 10.7151/dmgt.1420

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EMBEDDING COMPLETE TERNARY TREES INTO HYPERCUBES

S.A. Choudum  and  S. Lavanya

Department of Mathematics
Indian Institute of Technology Madras
Chennai 600 036, India
e-mail: sac@iitm.ac.in
e-mail: s.lavanya@yahoo.com

Abstract

We inductively describe an embedding of a complete ternary tree Th of height h into a hypercube Q of dimension at most ⎡(1.6)h⎤+1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of Th into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Th into its optimal hypercube with load 1 and dilation 2. The optimal hypercube has dimension ⎡(log23)h ⎤ ( = ⎡(1.585)h ⎤) or ⎡(log23)h⎤+1.

Keywords: complete ternary trees, hypercube, interconnection network, embedding, dilation, node congestion, edge congestion.

2000 Mathematics Subject Classification: 05C05, 05C90, 68E10.

References

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Received 24 October 2007
Revised 12 May 2008
Accepted 12 May 2008