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We have designed an algorithm for embedding of complete k-ary trees into 2-dimensional square meshes. The embedding has load 1, optimal dilation (the constant is 3 if k = 3 and 2 otherwise), and expansion 2. This solution can be easily converted into an embedding with optimal expansion &frac; for load 2 while keeping the dilation the same.

Embedding complete k-ary Trees into 2-dimensional meshes and tori