IEEE Transactions on Computers
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
Incomplete hypercubes: algorithms and embeddings
The Journal of Supercomputing
IEEE Transactions on Parallel and Distributed Systems
Embedding ladders and caterpillars into the hypercube
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
On embedding complete graphs into hypercubes
Discrete Mathematics
Discrete Applied Mathematics
The congestion of n-cube layout on a rectangular grid
Discrete Mathematics - Special issue on Selected Topics in Discrete Mathematics conferences
Embeddings of complete binary trees into grids and extended grids with total vertex-congestion
Discrete Applied Mathematics
Efficient embeddings of grids into grids
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Optimal embeddings of generalized ladders into hypercubes
Discrete Mathematics
Embedding complete trees into the hypercube
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Embedding Star Networks into Hypercubes
IEEE Transactions on Computers
Embedding of Hypercubes into Grids
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Degree constrained book embeddings
Journal of Algorithms
The circular wirelength problem for hypercubes
The circular wirelength problem for hypercubes
A survey of solved problems and applications on bandwidth, edgesum, and profile of graphs
Journal of Graph Theory
Topological Structure and Analysis of Interconnection Networks
Topological Structure and Analysis of Interconnection Networks
Minimum average congestion of enhanced and augmented hypercubes into complete binary trees
Discrete Applied Mathematics
Wirelength of 1-fault hamiltonian graphs into wheels and fans
Information Processing Letters
Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength
Discrete Applied Mathematics
Embedding of hypercubes into necklace, windmill and snake graphs
Information Processing Letters
Minimum wirelength of hypercubes into n-dimensional grid networks
Information Processing Letters
Wirelength of hypercubes into certain trees
Discrete Applied Mathematics
Embeddings of circulant networks
Journal of Combinatorial Optimization
Hi-index | 0.04 |
Grid embeddings are used not only to study the simulation capabilities of a parallel architecture but also to design its VLSI layout. In addition to dilation and congestion, wirelength is an important measure of an embedding. There are very few papers in the literature which provide the exact wirelength of grid embedding. As far as the most versatile architecture hypercube is concerned, only approximate estimates of the wirelength of grid embedding are available. In this paper, we give an exact formula of minimum wirelength of hypercube layout into grids and thereby we solve completely the wirelength problem of hypercubes into grids. We introduce a new technique to estimate the wirelength of a grid embedding. This new technique is based on a Congestion Lemma and a Partition Lemma which we study in this paper.