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Approximation of smallest linear tree grammar

Authors Artur Jez, Markus Lohrey

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Artur Jez
Markus Lohrey

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Artur Jez and Markus Lohrey. Approximation of smallest linear tree grammar. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 445-457, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(r^2.g.log(n)) 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 an approximation ratio polynomial in g. The analysis of the algorithm uses an extension of the recompression technique (used in the context of grammar-based string compression) from strings to trees.
  • Grammar-based compression
  • Tree compression
  • Tree-grammars


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