2026-07-22T04:54:15Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17702 2024-03-06T11:00:21Z ddc:004 open_access

Dynamic Data Structures for Parameterized String Problems Olkowski, Jędrzej Pilipczuk, Michał Rychlicki, Mateusz Węgrzycki, Karol Zych-Pawlewicz, Anna Parameterized algorithms Dynamic data structures String problems Closest String Edit Distance Disjoint Factors Predecessor problem 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jędrzej Olkowski and Michał Pilipczuk and Mateusz Rychlicki and Karol Węgrzycki and Anna Zych-Pawlewicz 2023 Is Part Of LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2023.50 urn:nbn:de:0030-drops-177026 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.50 eng https://creativecommons.org/licenses/by/4.0/legalcode