Algorithms and Complexity on Indexing Elastic Founder Graphs

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We study the problem of matching a string in a labeled graph. Previous research has shown that unless the Orthogonal Vectors Hypothesis (OVH) is false, one cannot solve this problem in strongly sub-quadratic time, nor index the graph in polynomial time to answer queries efficiently (Equi et al. ICALP 2019, SOFSEM 2021). These conditional lower-bounds cover even deterministic graphs with binary alphabet, but there naturally exist also graph classes that are easy to index: E.g. Wheeler graphs (Gagie et al. Theor. Comp. Sci. 2017) cover graphs admitting a Burrows-Wheeler transform -based indexing scheme. However, it is NP-complete to recognize if a graph is a Wheeler graph (Gibney, Thankachan, ESA 2019).
We propose an approach to alleviate the construction bottleneck of Wheeler graphs. Rather than starting from an arbitrary graph, we study graphs induced from multiple sequence alignments. Elastic degenerate strings (Bernadini et al. SPIRE 2017, ICALP 2019) can be seen as such graphs, and we introduce here their generalization: elastic founder graphs. We first prove that even such induced graphs are hard to index under OVH. Then we introduce two subclasses that are easy to index. Moreover, we give a near-linear time algorithm to construct indexable elastic founder graphs. This algorithm is based on an earlier segmentation algorithm for gapless multiple sequence alignments inducing non-elastic founder graphs (Mäkinen et al., WABI 2020), but uses more involved techniques to cope with repetitive string collections synchronized with gaps. Finally, we show that one of the subclasses admits a reduction to Wheeler graphs in polynomial time.
Original languageEnglish
Title of host publication32nd International Symposium on Algorithms and Computation (ISAAC 2021)
EditorsHee-Kap Ahn, Kunihiko Sadakane
Number of pages18
Place of PublicationDagstuhl, Germany
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publication date30 Nov 2021
ISBN (Electronic)978-3-95977-214-3
Publication statusPublished - 30 Nov 2021
MoE publication typeA4 Article in conference proceedings
EventThe 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
- Fukuoka, Japan
Duration: 6 Dec 20218 Dec 2021
Conference number: 32

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl – Leibniz-Zentrum für Informatik
ISSN (Electronic)1868-8969

Fields of Science

  • 113 Computer and information sciences

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