The approximation ratios of LZ78 and BISECTION are shown to be Θ((n/log n)^(2/3)) and Θ(sqrt(n/log n)), and the RePair lower bound is raised to Ω(log n/log log n).
On the complexity of opti mal grammar-based compres- sion
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The smallest grammar problem revisited
The approximation ratios of LZ78 and BISECTION are shown to be Θ((n/log n)^(2/3)) and Θ(sqrt(n/log n)), and the RePair lower bound is raised to Ω(log n/log log n).