Construction
All rotations of S$. Sort them. BWT = last column of sorted rotations. Encodes original + enables inverse.
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Inversion via LF-mapping
Rank of char c in last column = position of same char in first column. Follow to reconstruct.
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Compression
BWT clusters same chars. Run-length encode + move-to-front + entropy code = bzip2.
FM-index
BWT + rank/select structures → compressed substring search. Search pattern P in O(|P|). Basis of Bowtie/BWA in bioinformatics.