Algorithms and Complexity on Indexing Founder Graphs

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. ICAL...

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Bibliographic Details
Published in:Algorithmica Vol. 85; no. 6; pp. 1586 - 1623
Main Authors: Equi, Massimo, Norri, Tuukka, Alanko, Jarno, Cazaux, Bastien, Tomescu, Alexandru I., Mäkinen, Veli
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2023
Springer Nature B.V
Springer Verlag
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Burrows-Wheeler transform
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graphs
Indexing
Lower bounds
Mathematics of Computing
Polynomials
Special Issue on Algorithms and Computation (ISAAC 2021)
String matching
Theory of Computation
Compressed data structures
Multiple sequence alignment
String matching
Segmentation algorithms
Graph algorithms
Computational complexity
Pangenomics
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary: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: For example, 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 (MSAs). 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, repeat-free and semi-repeat-free graphs, that are easy to index. We give a linear time algorithm to construct a repeat-free (non-elastic) founder graph from a gapless MSA, and (parameterized) near-linear time algorithms to construct a semi-repeat-free (repeat-free, respectively) elastic founder graph from general MSA. Finally, we show that repeat-free founder graphs admit a reduction to Wheeler graphs in polynomial time.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-01007-w