On Maximal Repeats in Compressed Strings

Author Julian Pape-Lange

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Julian Pape-Lange
  • Technische Universität Chemnitz, Straße der Nationen 62, 09111 Chemnitz, Germany


I thank Professor Laurent Bartholdi for leading me to this research topic as well as for his helpful and inspiring pieces of advice.

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Julian Pape-Lange. On Maximal Repeats in Compressed Strings. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


This paper presents and proves a new non-trivial upper bound on the number of maximal repeats of compressed strings. Using Theorem 1 of Raffinot’s article "On Maximal Repeats in Strings", this upper bound can be directly translated into an upper bound on the number of nodes in the Compacted Directed Acyclic Word Graphs of compressed strings. More formally, this paper proves that the number of maximal repeats in a string with z (self-referential) LZ77-factors and without q-th powers is at most 3q(z+1)^3-2. Also, this paper proves that for 2000 <= z <= q this upper bound is tight up to a constant factor.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics on words
  • Mathematics of computing → Combinatoric problems
  • Maximal repeats
  • Combinatorics on compressed strings
  • LZ77
  • Compact suffix automata
  • CDAWGs


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