Random sequences from alphabet {1, . . . , r} are examined where repeated letters are allowed. Binary search trees are formed from these, and the average left-going depth of the first 1 is found. Next, the right-going depth of the first r is examined, and finally a merge (or ‘shuffle’) operator is used to obtain the average depth of an arbitrary node, which can be expressed in terms of the left...

We describe a sequential universal data compression procedure for binary tree sources that performs the " double mixture. " Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding distribution for tree sources with an unknown model and unknown parameters. Computational and ...

We study the embedding problem of enhanced and augmented hypercubes into complete binary trees. Using tree traversal techniques, we compute minimum average edge-congestion of enhanced and augmented hypercubes into complete binary trees.