Local decodability of the Burrows-Wheeler transform

Sandip Sinha, Omri Weinstein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


The Burrows-Wheeler Transform (BWT) is among the most influential discoveries in text compression and DNA storage. It is a reversible preprocessing step that rearranges an n-letter string into runs of identical characters (by exploiting context regularities), resulting in highly compressible strings, and is the basis of the bzip compression program. Alas, the decoding process of BWT is inherently sequential and requires Ω(n) time even to retrieve a single character. We study the succinct data structure problem of locally decoding short substrings of a given text under its compressed BWT, i.e., with small additive redundancy r over the Move-To-Front (bzip) compression. The celebrated BWT-based FM-index (FOCS’00), as well as other related literature, yield a trade-off of r = Õ(n/t) bits, when a single character is to be decoded in O(t) time. We give a near-quadratic improvement r = Õ(n lg(t)/t). As a by-product, we obtain an exponential (in t) improvement on the redundancy of the FM-index for counting pattern-matches on compressed text. In the interesting regime where the text compresses to o(n) (say, n/polylg(n)) bits, these results provide an exp(t) overall space reduction. For the local decoding problem of BWT, we also prove an Ω(n/t2) cell-probe lower bound for “symmetric" data structures. We achieve our main result by designing a compressed partial-sums (Rank) data structure over BWT. The key component is a locally-decodable Move-to-Front (MTF) code: with only O(1) extra bits per block of length nΩ(1), the decoding time of a single character can be decreased from Ω(n) to O(lg n). This result is of independent interest in algorithmic information theory.

Original languageAmerican English
Title of host publicationSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
EditorsMoses Charikar, Edith Cohen
PublisherAssociation for Computing Machinery
Number of pages12
ISBN (Electronic)9781450367059
StatePublished - 23 Jun 2019
Externally publishedYes
Event51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States
Duration: 23 Jun 201926 Jun 2019

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
© 2019 Association for Computing Machinery.


  • Burrows-wheeler transform
  • Cell-probe model
  • Local decoding
  • Pattern matching
  • Succinct data structures
  • Text compression


Dive into the research topics of 'Local decodability of the Burrows-Wheeler transform'. Together they form a unique fingerprint.

Cite this