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 NP -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.
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Accelerating Sequence Alignment to Graphs
Aligning DNA sequences to an annotated reference is a key step for genotyping in biology. Recent scientific studies have demonstrated improved inference by aligning reads to a variation graph, i.e., a reference sequence augmented with known genetic variations. Given a variation graph in the form of a directed acyclic string graph, the sequence to graph alignment problem seeks to find the best matching path in the graph for an input query sequence. Solving this problem exactly using a sequential dynamic programming algorithm takes quadratic time in terms of the graph size and query length, making it difficult to scale to high throughput DNA sequencing data. In this work, we propose the first parallel algorithm for computing sequence to graph alignments that leverages multiple cores and single-instruction multiple-data (SIMD) operations. We take advantage of the available inter-task parallelism, and provide a novel blocked approach to compute the score matrix while ensuring high memory locality. Using a 48-core Intel Xeon Skylake processor, the proposed algorithm achieves peak performance of 317 billion cell updates per second (GCUPS), and demonstrates near linear weak and strong scaling on up to 48 cores. It delivers significant performance gains compared to existing algorithms, and results in run-time reduction from multiple days to three hours for the problem of optimally aligning high coverage long (PacBio/ONT) or short (Illumina) DNA reads to an MHC human variation graph containing 10 million vertices.
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- Award ID(s):
- 1816027
- NSF-PAR ID:
- 10122207
- Date Published:
- Journal Name:
- IEEE International Parallel and Distributed Processing Symposium (IPDPS)
- Page Range / eLocation ID:
- 451 to 461
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Graph based non-linear reference structures such as variation graphs and colored de Bruijn graphs enable incorporation of full genomic diversity within a population. However, transitioning from a simple string-based reference to graphs requires addressing many computational challenges, one of which concerns accurately mapping sequencing read sets to graphs. Paired-end Illumina sequencing is a commonly used sequencing platform in genomics, where the paired-end distance constraints allow disambiguation of repeats. Many recent works have explored provably good index-based and alignment-based strategies for mapping individual reads to graphs. However, validating distance constraints efficiently over graphs is not trivial, and existing sequence to graph mappers rely on heuristics. We introduce a mathematical formulation of the problem, and provide a new algorithm to solve it exactly. We take advantage of the high sparsity of reference graphs, and use sparse matrix-matrix multiplications (SpGEMM) to build an index which can be queried efficiently by a mapping algorithm for validating the distance constraints. Effectiveness of the algorithm is demonstrated using real reference graphs, including a human MHC variation graph, and a pan-genome de-Bruijn graph built using genomes of 20 B. anthracis strains. While the one-time indexing time can vary from a few minutes to a few hours using our algorithm, answering a million distance queries takes less than a second.more » « less
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null (Ed.)Efficient and accurate alignment of DNA/RNA sequence reads to each other or to a reference genome/transcriptome is an important problem in genomic analysis. Nanopore sequencing has emerged as a major sequencing technology and many long-read aligners have been designed for aligning nanopore reads. However, the high error rate makes accurate and efficient alignment difficult. Utilizing the noise and error characteristics inherent in the sequencing process properly can play a vital role in constructing a robust aligner. In this article, we design QAlign, a pre-processor that can be used with any long-read aligner for aligning long reads to a genome/transcriptome or to other long reads. The key idea in QAlign is to convert the nucleotide reads into discretized current levels that capture the error modes of the nanopore sequencer before running it through a sequence aligner.We show that QAlign is able to improve alignment rates from around 80\% up to 90\% with nanopore reads when aligning to the genome. We also show that QAlign improves the average overlap quality by 9.2, 2.5 and 10.8\% in three real datasets for read-to-read alignment. Read-to-transcriptome alignment rates are improved from 51.6\% to 75.4\% and 82.6\% to 90\% in two real datasets.https://github.com/joshidhaivat/QAlign.git.Supplementary data are available at Bioinformatics online.more » « less
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Dyck-reachability is a fundamental formulation for program analysis, which has been widely used to capture properly-matched-parenthesis program properties such as function calls/returns and field writes/reads. Bidirected Dyck-reachability is a relaxation of Dyck-reachability on bidirected graphs where each edge u → ( i v labeled by an open parenthesis “( i ” is accompanied with an inverse edge v → ) i u labeled by the corresponding close parenthesis “) i ”, and vice versa. In practice, many client analyses such as alias analysis adopt the bidirected Dyck-reachability formulation. Bidirected Dyck-reachability admits an optimal reachability algorithm. Specifically, given a graph with n nodes and m edges, the optimal bidirected Dyck-reachability algorithm computes all-pairs reachability information in O ( m ) time. This paper focuses on the dynamic version of bidirected Dyck-reachability. In particular, we consider the problem of maintaining all-pairs Dyck-reachability information in bidirected graphs under a sequence of edge insertions and deletions. Dynamic bidirected Dyck-reachability can formulate many program analysis problems in the presence of code changes. Unfortunately, solving dynamic graph reachability problems is challenging. For example, even for maintaining transitive closure, the fastest deterministic dynamic algorithm requires O ( n 2 ) update time to achieve O (1) query time. All-pairs Dyck-reachability is a generalization of transitive closure. Despite extensive research on incremental computation, there is no algorithmic development on dynamic graph algorithms for program analysis with worst-case guarantees. Our work fills the gap and proposes the first dynamic algorithm for Dyck reachability on bidirected graphs. Our dynamic algorithms can handle each graph update ( i.e. , edge insertion and deletion) in O ( n ·α( n )) time and support any all-pairs reachability query in O (1) time, where α( n ) is the inverse Ackermann function. We have implemented and evaluated our dynamic algorithm on an alias analysis and a context-sensitive data-dependence analysis for Java. We compare our dynamic algorithms against a straightforward approach based on the O ( m )-time optimal bidirected Dyck-reachability algorithm and a recent incremental Datalog solver. Experimental results show that our algorithm achieves orders of magnitude speedup over both approaches.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IPDPS.2019.00055
