Approximation ratio of RePair

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 RePair algorithm from Ω( √ log n) to Ω(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.