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/
Grüttemeier, Niels ;
Komusiewicz, Christian ;
Morawietz, Nils ;
Sommer, Frank
String Factorizations Under Various Collision Constraints
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 |
