eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-03-03
50:1
50:22
10.4230/LIPIcs.STACS.2023.50
article
Dynamic Data Structures for Parameterized String Problems
Olkowski, Jędrzej
1
Pilipczuk, Michał
2
https://orcid.org/0000-0001-7891-1988
Rychlicki, Mateusz
3
https://orcid.org/0000-0002-8318-2588
Węgrzycki, Karol
4
5
https://orcid.org/0000-0001-9746-5733
Zych-Pawlewicz, Anna
2
https://orcid.org/0000-0002-5361-8969
Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland
Institute of Informatics, University of Warsaw, Poland
School of Computing, University of Leeds, UK
Saarland University, Saarbrücken, Germany
Max Planck Institute for Informatics, Saarbrücken, Germany
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently, our goal is to design a data structure that efficiently maintains a solution, or reports a lack thereof, upon updates in the instance.
We first consider the CLOSEST STRING problem, for which we design randomized dynamic data structures with amortized update times d^𝒪(d) and |Σ|^𝒪(d), respectively, where Σ is the alphabet and d is the assumed bound on the maximum distance. These are obtained by combining known static approaches to CLOSEST STRING with color-coding.
Next, we note that from a result of Frandsen et al. [J. ACM'97] one can easily infer a meta-theorem that provides dynamic data structures for parameterized string problems with worst-case update time of the form 𝒪_k(log log n), where k is the parameter in question and n is the length of the string. We showcase the utility of this meta-theorem by giving such data structures for problems DISJOINT FACTORS and EDIT DISTANCE. We also give explicit data structures for these problems, with worst-case update times 𝒪(k 2^k log log n) and 𝒪(k²log log n), respectively. Finally, we discuss how a lower bound methodology introduced by Amarilli et al. [ICALP'21] can be used to show that obtaining update time 𝒪(f(k)) for DISJOINT FACTORS and EDIT DISTANCE is unlikely already for a constant value of the parameter k.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol254-stacs2023/LIPIcs.STACS.2023.50/LIPIcs.STACS.2023.50.pdf
Parameterized algorithms
Dynamic data structures
String problems
Closest String
Edit Distance
Disjoint Factors
Predecessor problem