On the Complexity of Sequence-to-Graph Alignment

Abstract

Availability of extensive genetics data across multiple individuals and populations is driving the growing importance of graph based reference representations. Aligning sequences to graphs is a fundamental operation on several types of sequence graphs (variation graphs, assembly graphs, pan-genomes, etc.) and their biological applications. Though research on sequence to graph alignments is nascent, it can draw from related work on pattern matching in hypertext. In this paper, we study sequence to graph alignment problems under Hamming and edit distance models, and linear and affine gap penalty functions, for multiple variants of the problem that allow changes in query alone, graph alone, or in both. We prove that when changes are permitted in graphs either standalone or in conjunction with changes in the query, the sequence to graph alignment problem is N P-complete under both Hamming and edit distance models for alphabets of size ≥ 2. For the case where only changes to the sequence are permitted, we present an O(|V | + m|E|) time algorithm, where m denotes the query size, and V and E denote the vertex and edge sets of the graph, respectively. Our result is generalizable to both linear and affine gap penalty functions, and improves upon the run-time complexity of existing algorithms.

Accelerating Sequence Alignment to Graphs

“…Besides pan-genomics, PaSGAL can be useful for other applications that benefit from sequence to DAG alignment, e.g., sequence alignment to splicing graphs in transcriptomics [42] and antibiotic resistance profiling [43]. Future work includes development of intra-task algorithms for use-cases with small count of query sequences (e.g., when aligning assembly contigs to graphs), and extending this framework to accelerate the alignment to general sequence graphs [44]. Our algorithm combined with an appropriate graph localization heuristic could scale to variation graphs of complete vertebrae genomes.…”

SPAligner: Alignment of Long Diverged Molecular Sequences to Assembly Graphs

“…It worth to note that recently Jain et al [6] suggested an elegant algorithm extending the same time complexity to both linear and affine gap penalty functions.…”

“…Many popular short read assemblers [1, 2, 3] provide the user not only with a set of contig sequences, but also with assembly graphs, encoding the information on the potential adjacencies of the assembled sequences. Naturally arising problem of sequence-to-graph alignment has been a topic of many recent studies [4,5,6,7,8]. Identifying alignments of long error-prone reads (such as Pacbio and ONT reads) to assembly graphs is particularly important and has recently been applied to hybrid genome assembly [9,10], read error correction [11], and haplotype separation [12].…”

Validating Paired-end Read Alignments in Sequence Graphs

“…Similarly, there exist studies that have explored extension of the classic sequence-to-sequence alignment routines to graphs [19,20,30,36]. In our recent work [19], we presented new complexity results and algorithms for the alignment problem using general sequence-labeled graphs. The results show that a sequence (of length m) can be aligned to a labeled directed graph G(V, E) in O(|V | + m|E|) time, using commonly used scoring functions, while allowing edits in the query but not graph labels.…”

“…A few recent works have investigated extending Burrows-Wheeler-Transform-based indexing to sequence DAGs [41] and de-Bruijn graphs [2,29,40]. Similarly, there exist studies that have explored extension of the classic sequence-to-sequence alignment routines to graphs [19,20,30,36]. In our recent work [19], we presented new complexity results and algorithms for the alignment problem using general sequence-labeled graphs.…”