# 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

top- [1] S.L. Bezrukov, Embedding complete trees into the hypercube, Discrete Math. 110 (2001) 101-119, doi: 10.1016/S0166-218X(00)00256-0. Zbl0980.05022
- [2] A.K. Gupta, D. Nelson and H. Wang, Efficient embeddings of ternary trees into hypercubes, Journal of Parallel and Distributed Computing 63 (2003) 619-629, doi: 10.1016/S0743-7315(03)00037-6. Zbl1035.68081
- [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.
- [5] F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes (Morgan Kauffmann, San Mateo, CA, 1992). Zbl0743.68007
- [6] B. Monien and H. Sudbourough, Embedding one interconnection network into another, Computing Supplementary 7 (1990) 257-282.
- [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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