2026-07-24T23:15:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17961 2024-03-06T11:00:43Z ddc:004 open_access

Parameterized Algorithms for String Matching to DAGs: Funnels and Beyond Cáceres, Manuel string matching parameterized algorithms FPT inside P string algorithms graph algorithms directed acyclic graphs labeled graphs funnels The problem of String Matching to Labeled Graphs (SMLG) asks to find all the paths in a labeled graph G = (V, E) whose spellings match that of an input string S ∈ Σ^m. SMLG can be solved in quadratic O(m|E|) time [Amir et al., JALG 2000], which was proven to be optimal by a recent lower bound conditioned on SETH [Equi et al., ICALP 2019]. The lower bound states that no strongly subquadratic time algorithm exists, even if restricted to directed acyclic graphs (DAGs). In this work we present the first parameterized algorithms for SMLG on DAGs. Our parameters capture the topological structure of G. All our results are derived from a generalization of the Knuth-Morris-Pratt algorithm [Park and Kim, CPM 1995] optimized to work in time proportional to the number of prefix-incomparable matches. To obtain the parameterization in the topological structure of G, we first study a special class of DAGs called funnels [Millani et al., JCO 2020] and generalize them to k-funnels and the class ST_k. We present several novel characterizations and algorithmic contributions on both funnels and their generalizations. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Manuel Cáceres 2023 Is Part Of LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2023.7 urn:nbn:de:0030-drops-179619 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.7 eng https://creativecommons.org/licenses/by/4.0/legalcode