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R-enum: Enumeration of Characteristic Substrings in BWT-runs Bounded Space

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


We thank reviewers for their useful comments.

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Takaaki Nishimoto and Yasuo Tabei. R-enum: Enumeration of Characteristic Substrings in BWT-runs Bounded Space. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 21:1-21:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Enumerating characteristic substrings (e.g., maximal repeats, minimal unique substrings, and minimal absent words) in a given string has been an important research topic because there are a wide variety of applications in various areas such as string processing and computational biology. Although several enumeration algorithms for characteristic substrings have been proposed, they are not space-efficient in that their space-usage is proportional to the length of an input string. Recently, the run-length encoded Burrows-Wheeler transform (RLBWT) has attracted increased attention in string processing, and various algorithms for the RLBWT have been developed. Developing enumeration algorithms for characteristic substrings with the RLBWT, however, remains a challenge. In this paper, we present r-enum (RLBWT-based enumeration), the first enumeration algorithm for characteristic substrings based on RLBWT. R-enum runs in O(n log log (n/r)) time and with O(r log n) bits of working space for string length n and number r of runs in RLBWT. Here, r is expected to be significantly smaller than n for highly repetitive strings (i.e., strings with many repetitions). Experiments using a benchmark dataset of highly repetitive strings show that the results of r-enum are more space-efficient than the previous results. In addition, we demonstrate the applicability of r-enum to a huge string by performing experiments on a 300-gigabyte string of 100 human genomes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data compression
  • Enumeration algorithm
  • Burrows-Wheeler transform
  • Maximal repeats
  • Minimal unique substrings
  • Minimal absent words


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