Conversion from RLBWT to LZ77

Authors Takaaki Nishimoto, Yasuo Tabei

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Takaaki Nishimoto
  • RIKEN Center for Advanced Intelligence Project, Tokyo, Japan
Yasuo Tabei
  • RIKEN Center for Advanced Intelligence Project, Tokyo, Japan

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Takaaki Nishimoto and Yasuo Tabei. Conversion from RLBWT to LZ77. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler Transform (RLBWT) of a string into Lempel-Ziv 77 (LZ77) phrases of the reversed string. The first results with Policriti and Prezza’s conversion algorithm [Algorithmica 2018] were O(n log r) time and O(r) working space for length of the string n, number of runs r in the RLBWT, and number of LZ77 phrases z. Recent results with Kempa’s conversion algorithm [SODA 2019] are O(n / log n + r log^{9} n + z log^{9} n) time and O(n / log_{sigma} n + r log^{8} n) working space for the alphabet size sigma of the RLBWT. In this paper, we present a new conversion algorithm by improving Policriti and Prezza’s conversion algorithm where dynamic data structures for general purpose are used. We argue that these dynamic data structures can be replaced and present new data structures for faster conversion. The time and working space of our conversion algorithm with new data structures are O(n min{log log n, sqrt{(log r)/(log log r)}}) and O(r), respectively.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data compression
  • Burrows-Wheeler Transform
  • Lempel-Ziv Parsing
  • Lossless Data Compression


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