Communications of the ACM - Special section on computer architecture
The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
Optimal numberings of an N N array
SIAM Journal on Algebraic and Discrete Methods
Finding the minimum bandwidth of an interval graph
Information and Computation
Bandwidths and profiles of trees
Journal of Combinatorial Theory Series B
On Embedding Rectangular Grids in Hypercubes
IEEE Transactions on Computers
Mapping pyramid algorithms into hypercubes
Journal of Parallel and Distributed Computing
Bounds on minimax edge length for complete binary trees
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Problems in vlsi layout design
Problems in vlsi layout design
Executing Algorithms with Hypercube Topology on Torus Multicomputers
IEEE Transactions on Parallel and Distributed Systems
Hypercube Algorithms on Mesh Connected Multicomputers
IEEE Transactions on Parallel and Distributed Systems
Virtual Net: an efficient simulation for parallel computation
International Journal of Modelling and Simulation
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The authors formalize the problem of minimizing the length of the longest interprocessor wire as the problem of embedding the processors of a hypercube onto a rectangular mesh, so as to minimize the length of longest wire. Where neighboring nodes of the mesh are taken as being at unit distance from one another, and where wires are constrained to be laid out as horizontal and vertical wires, the length of the wire joining nodes u and v of the mesh equals the graph-theoretic distance between u and v. The problem of minimizing delays due to interprocessor communication is then modeled as the problem of embedding the vertices of a hypercube onto the nodes of a mesh, so as to minimize dilation. Two embeddings which achieve dilations that (for large n) are within 26% of the lower bound for square meshes and within 12% for meshes with aspect ratio 2 are presented.