Dense edge-disjoint embedding of complete binary trees in the hypercube

Abstract

We show that the complete binary tree with n > 8 leaves can be embedded in the hypercube with n nodes such that: paths of the tree are mapped onto edge-disjoint paths of the hypercube, at most two tree nodes (one of which is a leaf) are mapped onto each hypercube node, and the maximum distance from a leaf to the root of the tree is log 2 n + 1 hypercube edges (which is optimally short). This embedding facilitates efficient implementation of many P-RAM algorithms on the hypercube.