### Abstract

It has been proved that an incomplete binary tree cannot be embedded into an incomplete hypercube with dilation 1 and expansion 1. By applying some properties of inorder traversal, the authors present an embedding scheme with dilation 2, edgecongestion 2 and expansion ratio (N + l)/N, where N is the number of nodes in an incomplete binary tree. The authors prove that this embedding is optimal under the constraint of expansion ratio (N + l)/N. With this embedding scheme, a method is developed that can be used to simulate a binary tree on an incomplete hypercube effectively. Under the distributed environment, the mapping addresses of neighbouring nodes in an incomplete binary tree can be identified in constant time without repeating the mapping work. Furthermore, experimental results show that this scheme is much better than the corresponding best known dilation 1 embedding scheme in terms of hardware costs and implementation. Even in total time costs (addressing time, computation time and transmission time), this approach is quite competitive.

Original language | English |
---|---|

Pages (from-to) | 377-384 |

Number of pages | 8 |

Journal | IEE Proceedings: Computers and Digital Techniques |

Volume | 145 |

Issue number | 6 |

Publication status | Published - 1999 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*IEE Proceedings: Computers and Digital Techniques*,

*145*(6), 377-384.

}

*IEE Proceedings: Computers and Digital Techniques*, vol. 145, no. 6, pp. 377-384.

**Embedding incomplete binary trees into incomplete hypercubes.** / Huang, C. H.; Hsiao, Ju-Yuan; Lee, R. C.T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Embedding incomplete binary trees into incomplete hypercubes

AU - Huang, C. H.

AU - Hsiao, Ju-Yuan

AU - Lee, R. C.T.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - It has been proved that an incomplete binary tree cannot be embedded into an incomplete hypercube with dilation 1 and expansion 1. By applying some properties of inorder traversal, the authors present an embedding scheme with dilation 2, edgecongestion 2 and expansion ratio (N + l)/N, where N is the number of nodes in an incomplete binary tree. The authors prove that this embedding is optimal under the constraint of expansion ratio (N + l)/N. With this embedding scheme, a method is developed that can be used to simulate a binary tree on an incomplete hypercube effectively. Under the distributed environment, the mapping addresses of neighbouring nodes in an incomplete binary tree can be identified in constant time without repeating the mapping work. Furthermore, experimental results show that this scheme is much better than the corresponding best known dilation 1 embedding scheme in terms of hardware costs and implementation. Even in total time costs (addressing time, computation time and transmission time), this approach is quite competitive.

AB - It has been proved that an incomplete binary tree cannot be embedded into an incomplete hypercube with dilation 1 and expansion 1. By applying some properties of inorder traversal, the authors present an embedding scheme with dilation 2, edgecongestion 2 and expansion ratio (N + l)/N, where N is the number of nodes in an incomplete binary tree. The authors prove that this embedding is optimal under the constraint of expansion ratio (N + l)/N. With this embedding scheme, a method is developed that can be used to simulate a binary tree on an incomplete hypercube effectively. Under the distributed environment, the mapping addresses of neighbouring nodes in an incomplete binary tree can be identified in constant time without repeating the mapping work. Furthermore, experimental results show that this scheme is much better than the corresponding best known dilation 1 embedding scheme in terms of hardware costs and implementation. Even in total time costs (addressing time, computation time and transmission time), this approach is quite competitive.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032201962&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032201962

VL - 145

SP - 377

EP - 384

JO - IEE Proceedings: Computers and Digital Techniques

JF - IEE Proceedings: Computers and Digital Techniques

SN - 1350-2387

IS - 6

ER -