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Online LZ77 Parsing and Matching Statistics with RLBWTs

Authors Hideo Bannai , Travis Gagie, Tomohiro I



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Author Details

Hideo Bannai
  • Department of Informatics, Kyushu University, Japan, RIKEN Center for Advanced Intelligence Project, Japan
Travis Gagie
  • Diego Portales University and CeBiB, Chile
Tomohiro I
  • Frontier Research Academy for Young Researchers, Kyushu Institute of Technology, Japan

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Hideo Bannai, Travis Gagie, and Tomohiro I. Online LZ77 Parsing and Matching Statistics with RLBWTs. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 7:1-7:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CPM.2018.7

Abstract

Lempel-Ziv 1977 (LZ77) parsing, matching statistics and the Burrows-Wheeler Transform (BWT) are all fundamental elements of stringology. In a series of recent papers, Policriti and Prezza (DCC 2016 and Algorithmica, CPM 2017) showed how we can use an augmented run-length compressed BWT (RLBWT) of the reverse T^R of a text T, to compute offline the LZ77 parse of T in O(n log r) time and O(r) space, where n is the length of T and r is the number of runs in the BWT of T^R. In this paper we first extend a well-known technique for updating an unaugmented RLBWT when a character is prepended to a text, to work with Policriti and Prezza's augmented RLBWT. This immediately implies that we can build online the LZ77 parse of T while still using O(n log r) time and O(r) space; it also seems likely to be of independent interest. Our experiments, using an extension of Ohno, Takabatake, I and Sakamoto's (IWOCA 2017) implementation of updating, show our approach is both time- and space-efficient for repetitive strings. We then show how to augment the RLBWT further - albeit making it static again and increasing its space by a factor proportional to the size of the alphabet - such that later, given another string S and O(log log n)-time random access to T, we can compute the matching statistics of S with respect to T in O(|S| log log n) time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data compression
Keywords
  • Lempel-Ziv 1977
  • Matching Statistics
  • Run-Length Compressed Burrows-Wheeler Transform

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References

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