Why it matters

Wavelet tree is succinct workhorse. Understanding shapes advanced structures.

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The architecture

Binary tree partitioning alphabet.

Bit vectors at each level.

Rank / select via bit vectors.

Wavelet tree structureAlphabet splitrecursiveBit vectorsper levelRank + selectO(log sigma)Grossi et al. 2003; FM-index + succinct BWT enabled by wavelet trees
Wavelet tree.
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How it works end to end

Rank + select on bit vectors.

Compressed variants.

Applications: FM-index, RRR.