Embedding complete ternary trees into hypercubes
Discussiones Mathematicae Graph Theory (2008)
- Volume: 28, Issue: 3, page 463-476
- ISSN: 2083-5892
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topS.A. Choudum, and S. Lavanya. "Embedding complete ternary trees into hypercubes." Discussiones Mathematicae Graph Theory 28.3 (2008): 463-476. <http://eudml.org/doc/270307>.
@article{S2008,
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.},
author = {S.A. Choudum, S. Lavanya},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {complete ternary trees; hypercube; interconnection network; embedding; dilation; node congestion; edge congestion},
language = {eng},
number = {3},
pages = {463-476},
title = {Embedding complete ternary trees into hypercubes},
url = {http://eudml.org/doc/270307},
volume = {28},
year = {2008},
}
TY - JOUR
AU - S.A. Choudum
AU - S. Lavanya
TI - Embedding complete ternary trees into hypercubes
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 3
SP - 463
EP - 476
AB - 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.
LA - eng
KW - complete ternary trees; hypercube; interconnection network; embedding; dilation; node congestion; edge congestion
UR - http://eudml.org/doc/270307
ER -
References
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- [3] I. Havel, On certain trees in hypercube, in: R. Bodendick and R. Henn, eds, Topics in Combinatorics and Graph Theory (Physica-Verlag, Heidelberg, 1990) 353-358. Zbl0743.05016
- [4] X.J. Shen, Q. Hu and W.F. Liang, Embedding k-ary complete trees into hypercubes, Journal of Parallel and Distributed Computing 24 (1995) 100-106, doi: 10.1006/jpdc.1995.1010.
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- [7] J. Trdlicka and P. Tvrdík, Embedding of k-ary complete trees into hypercubes with uniform load, Journal of Parallel and Distributed Computing 52 (1998) 120-131, doi: 10.1006/jpdc.1998.1464. Zbl0911.68078
- [8] A.Y. Wu, Embedding of tree networks in hypercube, Journal of Parallel and Distributed Computing 2 (1985) 238-249, doi: 10.1016/0743-7315(85)90026-7.
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