Lossless compression of binary trees with correlated vertex names

Compression schemes for advanced data structures have become the challenge of today. Information theory has traditionally dealt with conventional data such as text, image, or video. In contrast, most data available today is multi-type and context dependent. To meet this challenge, we have recently initiated a systematic study of advanced data structures such as unlabeled graphs [1]. In this paper, we continue this program by considering trees with statistically correlated vertex names. Trees come in many forms, but here we deal with binary plane trees (where order of subtrees matters) and their non-plane version. Furthermore, we assume that each symbol of a vertex name depends in a Markovian sense on the corresponding symbol of the parent vertex name. We first evaluate the entropy for both types of trees. Then we propose for known sources two compression schemes COMPRESSPTREE for plane trees with correlated names, and COMPRESSNPTREE for non-plane trees. We show that these schemes achieve the lower bound within two bits.