# Efficient Embeddings into Hypercube-like Topologies

@article{Heun2003EfficientEI, title={Efficient Embeddings into Hypercube-like Topologies}, author={Volker Heun and Ernst W. Mayr}, journal={Comput. J.}, year={2003}, volume={46}, pages={632-644} }

Embeddings of various graph classes into hypercubes have been widely studied. Almost all these classes are regularly structured graphs such as meshes, complete trees or pyramids. In this paper, we present a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs. An extended edge bisector is an edge bisector with the additional property that a certain subset of the vertices is distributed more or less…

## 8 Citations

### Bounding Dilation and Edge-Congestion of Separator-Based Graph Embeddings into Grids

- Computer Science2015 Third International Symposium on Computing and Networking (CANDAR)
- 2015

It is proved that any graph with N nodes, maximum node degree Δ ≥ 2, and with a node-separator of size s, can be embedded with a dilation of O(N<sup>1/d</sup> log Δ / ϵ log N) and an edge-congestion of O (Δ) for any 1/log N ≤ ϵ <; 1 - α.

### Separator-based graph embedding into higher-dimensional grids with small congestion

- Computer Science2009 IEEE International Symposium on Circuits and Systems
- 2009

It is proved that any guest graph can be embedded with a smaller edge-congestion as the guest graph has a smaller separator, and as the host grid has a higher dimension.

### Separator-based graph embedding into multidimensional grids with small edge-congestion

- Computer Science, MathematicsDiscret. Appl. Math.
- 2015

### The bipanconnectivity and m-panconnectivity of the folded hypercube

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2007

### Embedding Hamiltonian Cycles in the Extended OTIS-n-Cube Topology

- Computer Science
- 2013

This paper introduces theoretical and practical study on embedding Hamiltonian cycle in the Extended OTIS-n-Cube and presents a generalized Algorithm, capable to form a Hamiltonian cycles starting from any node in the network.

### Hamiltonian cycle within extended OTIS-cube topology

- Computer Science
- 2011

This paper proposes an algorithm to form a Hamiltonian cycle in the extended OTIS-n-Cube Interconnection network and presents examples in different network sizes to show how Hamiltonian cycles are constructed.

### Interlacing Bypass Rings to Torus Networks for More Efficient Networks

- Computer ScienceIEEE Transactions on Parallel and Distributed Systems
- 2011

It is found that interlacing rings of sizes 6 and 12 to all three dimensions of a torus network with meshes 30 × 30 × 36 generate the best network of all possible networks, including 4D torus and hypercube of approximately 32,000 nodes.

### Broadcasting and Routing Algorithms for the Extended OTIS-Cube Network

- Computer Science

A routing algorithm for the Extended OTIS-n-Cube Networks is introduced, which has many good topological features such as regular degree, semantic structure, low diameter, and ability to embed graphs and cycles.

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