Approximation of smallest linear tree grammar
arXiv:1309.4958
Abstract
A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and r is the maximal rank of symbols in T (which is a constant in many applications). This is the first example of a grammar-based tree compression algorithm with a good, i.e. logarithmic in terms of the size of the input tree, approximation ratio. The analysis of the algorithm uses an extension of the recompression technique from strings to trees.
45 pages, published in Information and Computation. Approximation ratio improved since the first version, figures improved, some examples added. A small calculation error corrected since the previous version (all claims hold as previously)