2026-07-25T21:29:50Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12139 2024-03-06T10:49:24Z ddc:004 open_access

On Indeterminate Strings Matching Gawrychowski, Paweł Ghazawi, Samah Landau, Gad M. string matching indeterminate strings Cartesian trees order-preserving matching parameterized matching Given two indeterminate equal-length strings p and t with a set of characters per position in both strings, we obtain a determinate string p_w from p and a determinate string t_w from t by choosing one character per position. Then, we say that p and t match when p_w and t_w match for some choice of the characters. While the most standard notion of a match for determinate strings is that they are simply identical, in certain applications it is more appropriate to use other definitions, with the prime examples being parameterized matching, order-preserving matching, and the recently introduced Cartesian tree matching. We provide a systematic study of the complexity of string matching for indeterminate equal-length strings, for different notions of matching. We use n to denote the length of both strings, and r to be an upper-bound on the number of uncertain characters per position. First, we provide the first polynomial time algorithm for the Cartesian tree version that runs in deterministic 𝒪(nlog² n) and expected 𝒪(nlog nlog log n) time using 𝒪(nlog n) space, for constant r. Second, we establish NP-hardness of the order-preserving version for r=2, thus solving a question explicitly stated by Henriques et al. [CPM 2018], who showed hardness for r=3. Third, we establish NP-hardness of the parameterized version for r=2. As both parameterized and order-preserving indeterminate matching reduce to the standard determinate matching for r=1, this provides a complete classification for these three variants. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Paweł Gawrychowski and Samah Ghazawi and Gad M. Landau 2020 Is Part Of LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2020.14 urn:nbn:de:0030-drops-121393 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.14 eng https://creativecommons.org/licenses/by/3.0/legalcode