Computing MEMs on Repetitive Text Collections

Author Gonzalo Navarro

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Author Details

Gonzalo Navarro
  • Center for Biotechnology and Bioengineering (CeBiB), Santiago, Chile
  • Department of Computer Science, University of Chile, Santiago, Chile

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Gonzalo Navarro. Computing MEMs on Repetitive Text Collections. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern P[1..m] on a large repetitive text collection T[1..n], which is represented as a (hopefully much smaller) run-length context-free grammar of size g_{rl}. We show that the problem can be solved in time O(m² log^ε n), for any constant ε > 0, on a data structure of size O(g_{rl}). Further, on a locally consistent grammar of size O(δ log n/δ), the time decreases to O(m log m(log m + log^ε n)). The value δ is a function of the substring complexity of T and Ω(δ log n/δ) is a tight lower bound on the compressibility of repetitive texts T, so our structure has optimal size in terms of n and δ.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • grammar-based indices
  • maximal exact matches
  • locally consistent grammars
  • substring complexity


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