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arXiv · 1703.06061

Approximation ratio of RePair

Danny Hucke·Artur Jez·Markus Lohrey
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Abstract

In a seminal paper of Charikar et al.~on the smallest grammar problem, the authors derive upper and lower bounds on the approximation ratios for several grammar-based compressors. Here we improve the lower bound for the famous {\sf RePair} algorithm from $\Omega(\sqrt{\log n})$ to $\Omega(\log n/\log\log n)$. The family of words used in our proof is defined over a binary alphabet, while the lower bound from Charikar et al. needs an alphabet of logarithmic size in the length of the provided words.

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Danny Hucke, Artur Jez, Markus Lohrey. 2017-03-17. Approximation ratio of RePair. https://arxiv.org/abs/1703.06061

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