A Compact Layout for the Three-Dimensional Tree of Meshes

Document Type

Article

Publication Date

1988

Publication Title

Applied Mathematics Letters

Volume

1

Issue

2

Pages

171-176

Publisher Name

Elsevier

Abstract

We provide a simple demonstration that the n×n×n tree of meshes graph truncated to llevels can be embedded in a three-dimensional (3D) grid using volume . The maximum wire length in the embedding of the graph is . This embedding simplifies the method developed by Leighton and Rosenberg [6] for the 3D embeddings of general graphs and allows the framework of Bhatt and Leighton [1] for 2D graph layout to be extended to 3D. It also leads to good 3D layouts for various fat-tree routing networks [8,2] and the 3D meshes of trees graph [5].

Comments

Author Posting. © Elsevier 1988. This article is posted here for personal use, not for redistribution. The article was published in Applied Mathematics Letters, vol. 1, no. 2, 1988, https://doi.org/10.1016/0893-9659(88)90066-3

See also erratum that can be found at http://ecommons.luc.edu/cs_facpubs/89

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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