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We present an embedding of the complete binary tree with n leaves in the Vn x Vn mesh, for any n = 2exp(2m) where m is a positive integer. The embedding has the following properties: at most two tree nodes (one of which is a leaf) are mapped onto each mesh node, paths of the tree are mapped onto edge-disjoint paths in the mesh (each mesh edge considered as two anti-parallel directed edges) and the maximum distance from a leaf to the root of the tree is Vn + O (log n) mesh steps. This embedding facilitates efficient implementation of many P-RAM algorithms on the mesh, particularly those using the balanced binary tree technique. Such an embedding offers greater flexibility of use and improves the time complexity of these implementations by a constant factor compared with previously described embeddings.

Dense edge-disjoint embedding of binary trees in the mesh