# Embedding Variants of Hypercubes with Dilation 2

@article{Manuel2012EmbeddingVO, title={Embedding Variants of Hypercubes with Dilation 2}, author={Paul D. Manuel and Indra Rajasingh and R. Sundara Rajan}, journal={J. Interconnect. Networks}, year={2012}, volume={13} }

Graph embedding has been known as a powerful tool for implementation of parallel algorithms and simulation of interconnection networks. In this paper, we introduce a technique to obtain a lower bound for the dilation of an embedding. Moreover, we give algorithms for embedding variants of hypercubes with dilation 2 proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding folded hypercubes and augmented cubes into hypercubes.

## 11 Citations

### A Tight Bound for Congestion of an Embedding

- Computer ScienceCALDAM
- 2015

A technique to obtain a tight bound for congestion of an embedding is introduced and algorithms to compute exact congestion of embedding the hypercubes into the cylinder and the torus are given.

### A Lower Bound for Dilation of an Embedding

- Computer ScienceComput. J.
- 2015

Algorithms to compute exact dilation of embedding circulant network into a triangular grid, Tower of Hanoi graph and Sierpinski gasket graph are given, proving that the lower bound obtained is sharp.

### Embeddings Between Hypercubes and Hypertrees

- Computer ScienceJ. Graph Algorithms Appl.
- 2015

The rooted hypertree RHT (r) is embedded into r-dimensional hypercube Q r with dilation 2, r 2 and the exact wirelength is computed.

### Lower bounds for dilation, wirelength, and edge congestion of embedding graphs into hypercubes

- Computer ScienceJ. Supercomput.
- 2021

Lower bounds for the dilation, wirelength, and edge congestion of an embedding of a graph into a hypercube are proved and two of these bounds are expressed in terms of the bisection width.

### Improved Bound for Dilation of an Embedding onto Circulant Networks

- Computer ScienceTrends in Mathematics
- 2019

Algorithms to compute dilation of embedding circulant network into certain trees, for instance, m-rooted complete binary tree, m -rooted sibling tree, and r-dimensional hypertree are provided, proving that the improved bound obtained is sharp.

### EXACT WIRELENGTH OF EMBEDDING THE HYPERCUBES INTO CYCLE-OF-LADDERS

- Computer Science
- 2013

This paper presents an algorithm to compute the exact wirelength of embedding the hypercubes into cycle-of-ladders and proves its correctness.

### Embedding of Hypercubes into l-Sibling Trees

- Computer ScienceJ. Interconnect. Networks
- 2013

A tree called l-sibling trees is introduced and an O(r)-linear time algorithm is provided to compute the minimum wirelength of embedding r- dimensional hypercube into r-dimensional l-Sibling tree.

### Embedding Circulant Networks into Butterfly and Benes Networks

- Computer ScienceIWOCA
- 2014

The minimum dilation of embedding circulant networks into butterfly and benes networks is computed and it is shown that the embedding with a long dilation faces many problems, such as long communication delay, coupling problems and the existence of different types of uncontrolled noise.

### A Linear Time Algorithm for Embedding Christmas Trees into Certain Trees

- Computer ScienceParallel Process. Lett.
- 2015

An algorithm for embedding Christmas trees into caterpillars with dilation 3 proving that the lower bound obtained in [30] is sharp is presented and a linear time algorithm is provided to compute the exact wirelength.

### EMBEDDING OF CIRCULANT NETWORKS INTO $k$-ROOTED SIBLING TREES

- Computer Science
- 2013

This paper determines the exact wirelength and dilation of embedding circulant networks into k-rooted sibling trees into parallel computer architectures.

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