Abstract
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 subquadratic time, nor index the graph in polynomial time to answer queries efficiently (Equi et al. ICALP 2019, SOFSEM 2021). These conditional lowerbounds 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 BurrowsWheeler transform based indexing scheme. However, it is NPcomplete 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 nearlinear time algorithm to construct indexable elastic founder graphs. This algorithm is based on an earlier segmentation algorithm for gapless multiple sequence alignments inducing nonelastic 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.
BibTeX  Entry
@InProceedings{equi_et_al:LIPIcs.ISAAC.2021.20,
author = {Equi, Massimo and Norri, Tuukka and Alanko, Jarno and Cazaux, Bastien and Tomescu, Alexandru I. and M\"{a}kinen, Veli},
title = {{Algorithms and Complexity on Indexing Elastic Founder Graphs}},
booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
pages = {20:120:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959772143},
ISSN = {18688969},
year = {2021},
volume = {212},
editor = {Ahn, HeeKap and Sadakane, Kunihiko},
publisher = {Schloss Dagstuhl  LeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15453},
URN = {urn:nbn:de:0030drops154532},
doi = {10.4230/LIPIcs.ISAAC.2021.20},
annote = {Keywords: orthogonal vectors hypothesis, multiple sequence alignment, segmentation}
}
Keywords: 

orthogonal vectors hypothesis, multiple sequence alignment, segmentation 
Collection: 

32nd International Symposium on Algorithms and Computation (ISAAC 2021) 
Issue Date: 

2021 
Date of publication: 

30.11.2021 