Optimal Embedding of Complete Binary Trees into Lines and Grids

We consider several graph embedding problems which have a lot of important applications in parallel and distributed computing and which have been unsolved so far. Our major result is that the complete binary tree can be embedded into the square grid of the same size with almost optimal dilation (up to a very small factor). To achieve this, we first state an embedding of the complete binary tree into the line with optimal dilation.

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