[서평]「Algorithms on Strings, Trees, and Sequences」

There has been significant recent interest in parallel frameworks for processing graphs due to their applicability in studying social networks, the Web graph, networks in biology, and unstructured meshes in scientific simulation. Due to the desire to process large graphs, these systems have emphasized the ability to run on distributed memory machines. Today, however, a single multicore server can support more than a terabyte of memory, which can fit graphs with tens or even hundreds of billions of edges. Furthermore, for graph algorithms, shared-memory multicores are generally significantly more efficient on a per core, per dollar, and per joule basis than distributed memory systems, and shared-memory algorithms tend to be simpler than their distributed counterparts.In this paper, we present a lightweight graph processing framework that is specific for shared-memory parallel/multicore machines, which makes graph traversal algorithms easy to write. The framework has two very simple routines, one for mapping over edges and one for mapping over vertices. Our routines can be applied to any subset of the vertices, which makes the framework useful for many graph traversal algorithms that operate on subsets of the vertices. Based on recent ideas used in a very fast algorithm for breadth-first search (BFS), our routines automatically adapt to the density of vertex sets. We implement several algorithms in this framework, including BFS, graph radii estimation, graph connectivity, betweenness centrality, PageRank and single-source shortest paths. Our algorithms expressed using this framework are very simple and concise, and perform almost as well as highly optimized code. Furthermore, they get good speedups on a 40-core machine and are significantly more efficient than previously reported results using graph frameworks on machines with many more cores.

Ligra: a lightweight graph processing framework for shared memory

Reference genomes guide our interpretation of DNA sequence data. However, conventional linear references represent only one version of each locus, ignoring variation in the population. Poor representation of an individual's genome sequence impacts read mapping and introduces bias. Variation graphs are bidirected DNA sequence graphs that compactly represent genetic variation across a population, including large-scale structural variation such as inversions and duplications. Previous graph genome software implementations have been limited by scalability or topological constraints. Here we present vg, a toolkit of computational methods for creating, manipulating, and using these structures as references at the scale of the human genome. vg provides an efficient approach to mapping reads onto arbitrary variation graphs using generalized compressed suffix arrays, with improved accuracy over alignment to a linear reference, and effectively removing reference bias. These capabilities make using variation graphs as references for DNA sequencing practical at a gigabase scale, or at the topological complexity of de novo assemblies.

/pdf/variation-graph-toolkit-improves-read-mapping-by-b8gf23n8qw.pdf

Variation graph toolkit improves read mapping by representing genetic variation in the reference.

The recent advances in sequencing technologies enable the assembly of individual genomes to the quality of the reference genome. How to integrate multiple genomes from the same species and make the integrated representation accessible to biologists remains an open challenge. Here, we propose a graph-based data model and associated formats to represent multiple genomes while preserving the coordinate of the linear reference genome. We implement our ideas in the minigraph toolkit and demonstrate that we can efficiently construct a pangenome graph and compactly encode tens of thousands of structural variants missing from the current reference genome.

/pdf/the-design-and-construction-of-reference-pangenome-graphs-996hc42t9j.pdf

The design and construction of reference pangenome graphs with minigraph

BACKGROUND: The domestic pig (Sus scrofa) is important both as a food source and as a biomedical model given its similarity in size, anatomy, physiology, metabolism, pathology, and pharmacology to humans. The draft reference genome (Sscrofa10.2) of a purebred Duroc female pig established using older clone-based sequencing methods was incomplete, and unresolved redundancies, short-range order and orientation errors, and associated misassembled genes limited its utility. RESULTS: We present 2 annotated highly contiguous chromosome-level genome assemblies created with more recent long-read technologies and a whole-genome shotgun strategy, 1 for the same Duroc female (Sscrofa11.1) and 1 for an outbred, composite-breed male (USMARCv1.0). Both assemblies are of substantially higher (>90-fold) continuity and accuracy than Sscrofa10.2. CONCLUSIONS: These highly contiguous assemblies plus annotation of a further 11 short-read assemblies provide an unprecedented view of the genetic make-up of this important agricultural and biomedical model species. We propose that the improved Duroc assembly (Sscrofa11.1) become the reference genome for genomic research in pigs.

/pdf/an-improved-pig-reference-genome-sequence-to-enable-pig-sv01sf8133.pdf

An improved pig reference genome sequence to enable pig genetics and genomics research

Engineering efficient implementations of compact and succinct structures is time-consuming and challenging, since there is no standard library of easy-to-use, highly optimized, and composable components. One consequence is that measuring the practical impact of new theoretical proposals is difficult, since older baseline implementations may not rely on the same basic components, and reimplementing from scratch can be time-consuming. In this paper we present a framework for experimentation with succinct data structures, providing a large set of configurable components, together with tests, benchmarks, and tools to analyze resource requirements. We demonstrate the functionality of the framework by recomposing two succinct solutions for top-k document retrieval which can operate on both character and integer alphabets.

From Theory to Practice: Plug and Play with Succinct Data Structures

MOTIVATION Low-cost genome sequencing gives unprecedented complete information about the genetic structure of populations, and a population graph captures the variations between many individuals of a population. Recently, Marcus et al. proposed to use a compressed de Bruijn graph for representing an entire population of genomes. They devised an O(n log g) time algorithm called splitMEM that constructs this graph directly (i.e. without using the uncompressed de Bruijn graph) based on a suffix tree, where n is the total length of the genomes and g is the length of the longest genome. Since the applicability of their algorithm is limited to rather small datasets, there is a strong need for space-efficient construction algorithms. RESULTS We present two algorithms that outperform splitMEM in theory and in practice. The first implements a novel linear-time suffix tree algorithm by means of a compressed suffix tree. The second algorithm uses the Burrows-Wheeler transform to build the compressed de Bruijn graph in [Formula: see text] time, where σ is the size of the alphabet. To demonstrate the scalability of the algorithms, we applied it to seven human genomes. AVAILABILITY AND IMPLEMENTATION https://www.uni-ulm.de/in/theo/research/seqana/.

Graphical pan-genome analysis with compressed suffix trees and the Burrows–Wheeler transform

Many sequence analysis tasks can be accomplished with a suffix array, and several of them additionally need the longest common prefix array. In large scale applications, suffix arrays are being replaced with full-text indexes that are based on the Burrows-Wheeler transform. In this paper, we present the first algorithm that computes the longest common prefix array directly on the wavelet tree of the Burrows-Wheeler transformed string. It runs in linear time and a practical implementation requires approximately 2.2 bytes per character.

Computing the longest common prefix array based on the burrows-wheeler transform

The Burrows-Wheeler transform (BWT), originally invented for data compression, is nowadays also the core of many self-indexes, which can be used to solve many problems in bioinformatics. However, the memory requirement during the construction of the BWT is often the bottleneck in applications in the bioinformatics domain.

In this paper, we present a linear-time semi-external algorithm whose memory requirement is only about one byte per input symbol. Our experiments show that this algorithm provides a new time-memory trade-off between external and in-memory construction algorithms.

Space-Efficient Construction of the Burrows-Wheeler Transform

Recently, Marcus et al. (Bioinformatics 30:3476–83, 2014) proposed to use a compressed de Bruijn graph to describe the relationship between the genomes of many individuals/strains of the same or closely related species. They devised an $$O(n\log g)$$
 time algorithm called splitMEM that constructs this graph directly (i.e., without using the uncompressed de Bruijn graph) based on a suffix tree, where n is the total length of the genomes and g is the length of the longest genome. Baier et al. (Bioinformatics 32:497–504, 2016) improved their result. In this paper, we propose a new space-efficient representation of the compressed de Bruijn graph that adds the possibility to search for a pattern (e.g. an allele—a variant form of a gene) within the pan-genome. The ability to search within the pan-genome graph is of utmost importance and is a design goal of pan-genome data structures.

/pdf/a-representation-of-a-compressed-de-bruijn-graph-for-pan-3ob5xdlvkl.pdf

A representation of a compressed de Bruijn graph for pan-genome analysis that enables search.

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