# A New Efficient Algorithm for Embedding an Arbitrary Binary Tree into Its Optimal Hypercube

@article{Heun1996ANE, title={A New Efficient Algorithm for Embedding an Arbitrary Binary Tree into Its Optimal Hypercube}, author={Volker Heun and Ernst W. Mayr}, journal={J. Algorithms}, year={1996}, volume={20}, pages={375-399} }

Thed-dimensional binary hypercube is a very popular model of parallel computation. On the other hand, the execution of many algorithms can be represented by binary trees, making it desirable to simulate binary trees on a hypercube. In this paper, we present a simple one-to-one embedding of arbitrary binary trees into their optimal hypercubes with dilation 8 and constant node-congestion. The novelty of our method is the use of an intermediate quadtree data structure, which also permits the…

## 17 Citations

### Efficient Dynamic Embedding of Arbitrary Binary Trees into Hypercubes

- Computer ScienceIRREGULAR
- 1996

The algorithm presented here uses migration of previously mapped tree vertices and achieves dilation 9, unit load, expansion <4 and constant node-congestion and the embedding can be computed on the hypercube.

### Optimal Dynamic Embeddings of Complete Binary Trees into Hypercubes

- Computer ScienceJ. Parallel Distributed Comput.
- 2001

This paper presents simple dynamic embeddings of double-rooted complete binary trees into hypercubes which do not suffer from this disadvantage and also presents edge-disjointembeddings with optimal load and unit dilation.

### Efficient Dynamic Embeddings of Binary Trees into Hypercubes

- Computer ScienceJ. Algorithms
- 2002

A deterministic algorithm for dynamically embedding binary trees into hypercubes using migration of previously mapped tree vertices constructs a dynamic embedding which achieves dilation of at most 9, unit load, nearly optimal expansion, and constant edge- and node-congestion simultaneously.

### Embedding Graphs with Bounded Treewidth into Optimal Hypercubes

- Computer Science, MathematicsSTACS
- 1996

This is the first time that embeddings of graphs with a very irregular structure into hypercubes are investigated and a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube is presented.

### Optimal Tree Contraction and Term Matching on the Hypercube and Related Networks

- Computer ScienceAlgorithmica
- 1997

The algorithm is based on novel routing techniques and, for certain small subtrees, simulates optimal PRAM algorithms and can be used to solve the term matching problem, one of the fundamental problems in logic programming.

### A General Method for Efficient Embeddings of Graphs into Optimal Hypercubes

- Computer Science, MathematicsEuro-Par, Vol. I
- 1996

This paper presents a general method for one-to-one embedding irregular graphs into their optimal hypercubes based on extended-edge-bisectors of graphs.

### On embedding binary trees into hypercubes

- Computer Science, Mathematics
- 2000

It is shown that a 2n- vertex balanced one-legged caterpillar with leg length of at most 2 can be embedded into an n-dimensional cube with dilation 1, and that an N-vertex binary tree with proper pathwidth of at least 2 can been embedded into a ⌈log N⌉-dimensional cubes with dilated dilation 2.

### Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes

- Computer Science, MathematicsJ. Algorithms
- 2002

This is the first time that embeddings of graphs with a highly irregular structure into hypercubes are investigated and the presented embedding achieves dilation of at most 3?log((d+1)(t+1))?+8 and node-congestion of at least O(d(dt)3), where t denotes the treewidth of the graph.

### Efficient Embeddings into Hypercube-like Topologies

- Computer Science, MathematicsComput. J.
- 2003

This paper presents a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs, and it is shown that if the extended bisection can be computed efficiently on the hypercube, then so can the embedding.

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