Revisiting (Bijective) Burrows-Wheeler Transform Space-Time Trade-Off Constructions

The bijective Burrows-Wheeler transform (BBWT) replaces the delimiter of the ordinary BWT by a Lyndon factorization and sorts factor conjugates in $ω$-order. It admits quadratic-time constant-workspace algorithms and linear-time linear-space algorithms. We extend the small-space BWT trade-off of Crochemore et al. [JDA,'15] to the BBWT and accelerate both constructions. For $τ\in [3..n]$, let $σ_τ\le\min(σ,τ+1)$ be the maximum construction-batch alphabet size. We construct either transform in $ O\!\left( \frac{n^2}τ \frac{\logτ}{\log\logτ} \right) $ time and $O(τσ_τ)$ additional space, assuming $τσ_τ=O(n)$. This improves the transferred $O((n^2/τ)\logτ)$ bound by a $\log\logτ$ factor. If $σ_τ\in w^{O(1)}$, where $w\inΩ(\log n)$ is the word size, the time improves to $ O\!\left( \frac{n^2}τ + \frac{n\logτ}{\log\logτ} \right). $ For inversion, the same bounds hold with the global alphabet size $σ$ in place of $σ_τ$.