English

Approximation ratio of RePair

Data Structures and Algorithms 2017-03-20 v1

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 Ω(logn)\Omega(\sqrt{\log n}) to Ω(logn/loglogn)\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.

Keywords

Cite

@article{arxiv.1703.06061,
  title  = {Approximation ratio of RePair},
  author = {Danny Hucke and Artur Jez and Markus Lohrey},
  journal= {arXiv preprint arXiv:1703.06061},
  year   = {2017}
}
R2 v1 2026-06-22T18:48:57.527Z