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String Factorizations Under Various Collision Constraints

Authors Niels Grüttemeier , Christian Komusiewicz , Nils Morawietz, Frank Sommer

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Author Details

Niels Grüttemeier
  • Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany
Christian Komusiewicz
  • Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany
Nils Morawietz
  • Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany
Frank Sommer
  • Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany

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Niels Grüttemeier, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. String Factorizations Under Various Collision Constraints. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 17:1-17:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


In the NP-hard Equality-Free String Factorization problem, we are given a string S and ask whether S can be partitioned into k factors that are pairwise distinct. We describe a randomized algorithm for Equality-Free String Factorization with running time 2^k⋅ k^{𝒪(1)}+𝒪(n) improving over previous algorithms with running time k^{𝒪(k)}+𝒪(n) [Schmid, TCS 2016; Mincu and Popa, Proc. SOFSEM 2020]. Our algorithm works for the generalization of Equality-Free String Factorization where equality can be replaced by an arbitrary polynomial-time computable equivalence relation on strings. We also consider two factorization problems to which this algorithm does not apply, namely Prefix-Free String Factorization where we ask for a factorization of size k such that no factor is a prefix of another factor and Substring-Free String Factorization where we ask for a factorization of size k such that no factor is a substring of another factor. We show that these two problems are NP-hard as well. Then, we show that Prefix-Free String Factorization with the prefix-free relation is fixed-parameter tractable with respect to k by providing a polynomial problem kernel. Finally, we show a generic ILP formulation for R-Free String Factorization where R is an arbitrary relation on strings. This formulation improves over a previous one for Equality-Free String Factorization in terms of the number of variables.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Pattern matching
  • NP-hard problem
  • fixed-parameter algorithms
  • collision-aware string partitioning


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