  We use the traveling front approach to derive exact asymptotic results for
the statistics of the number of particles in a class of directed diffusion
limited aggregation models on a Cayley tree. We point out that some aspects of
these models are closely connected to two different problems in computer
science, namely the digital search tree problem in data structures and the
Lempel-Ziv algorithm for data compression. The statistics of the number of
particles studied here is related to the statistics of height in digital search
trees which, in turn, is related to the statistics of the length of the longest
word formed by the Lempel-Ziv algorithm. Implications of our results to these
computer science problems are pointed out.
