License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2020.17
URN: urn:nbn:de:0030-drops-121428
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12142/
Go to the corresponding LIPIcs Volume Portal


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

String Factorizations Under Various Collision Constraints

pdf-format:
LIPIcs-CPM-2020-17.pdf (0.5 MB)


Abstract

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^{?(1)}+?(n) improving over previous algorithms with running time k^{?(k)}+?(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.

BibTeX - Entry

@InProceedings{grttemeier_et_al:LIPIcs:2020:12142,
  author =	{Niels Gr{\"u}ttemeier and Christian Komusiewicz and Nils Morawietz and Frank Sommer},
  title =	{{String Factorizations Under Various Collision Constraints}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{Inge Li G{\o}rtz and Oren Weimann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12142},
  URN =		{urn:nbn:de:0030-drops-121428},
  doi =		{10.4230/LIPIcs.CPM.2020.17},
  annote =	{Keywords: NP-hard problem, fixed-parameter algorithms, collision-aware string partitioning}
}

Keywords: NP-hard problem, fixed-parameter algorithms, collision-aware string partitioning
Collection: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Issue Date: 2020
Date of publication: 09.06.2020


DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI