Optimal Dynamic Embeddings of Complete Binary Trees Into Hypercubes

TitleOptimal Dynamic Embeddings of Complete Binary Trees Into Hypercubes
Publication TypeTechnical Report
Year of Publication1998
AuthorsHeun V, Mayr EW
Other Numbers1142
KeywordsComplete Binary Trees, Graph Embeddings, Hypercubes, Simulation of Algorithms

The double-rooted complete binary tree is a complete binary tree where the root is replaced by an edge. It is folklore that the double-rooted complete binary tree is a spanning tree of the hypercube of the same size. Unfortunately, the usual construction of an embedding of a double-rooted complete binary tree into the hypercube does not provide any hint how this embedding can be extended if each leaf spawns two new leaves. In this paper, we present simple dynamic embeddings of double-rooted complete binary trees into hypercubes which do not suffer from this disadvantage. We also present edge-disjoint embeddings of large binary trees with optimal load and unit dilation. Furthermore, all these embeddings can be efficiently implemented on the hypercube itself such that the embedding of each new level of leaves can be computed in constant time. Since complete binary trees are similar to double-rooted complete binary trees, our results can be immediately transfered to complete binary trees.

Bibliographic Notes

ICSI Technical Report TR-98-022

Abbreviated Authors

V. Heun and E. W. Mayr

ICSI Publication Type

Technical Report