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arXiv · 1309.4958

Approximation of smallest linear tree grammar

Artur Jeż·Markus Lohrey
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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.

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Artur Jeż, Markus Lohrey. 2013-09-19. Approximation of smallest linear tree grammar. https://arxiv.org/abs/1309.4958

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