eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-09
17:1
17:14
10.4230/LIPIcs.CPM.2020.17
article
String Factorizations Under Various Collision Constraints
Grüttemeier, Niels
1
https://orcid.org/0000-0002-6789-2918
Komusiewicz, Christian
1
https://orcid.org/0000-0003-0829-7032
Morawietz, Nils
1
Sommer, Frank
1
https://orcid.org/0000-0003-4034-525X
Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol161-cpm2020/LIPIcs.CPM.2020.17/LIPIcs.CPM.2020.17.pdf
NP-hard problem
fixed-parameter algorithms
collision-aware string partitioning