[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

Concrete mathematics, a foundation for computer science, by Ronald L. Graham, Donald E. Knuth and Oren Patashnik. Pp 625. £24·95. 1989. ISBN 0-201-14236-8 (Addison-Wesley)

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.

On-line construction of suffix trees

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

Exact string matching is a problem that computer programmers face on a regular basis, and full-text indexes like the suffix tree or the suffix array provide fast string search over large texts. In the last decade, research on compressed indexes has flourished because the main problem in large-scale applications is the space consumption of the index. Nowadays, the most successful compressed indexes are able to obtain almost optimal space and search time simultaneously. It is known that a myriad of sequence analysis and comparison problems can be solved efficiently with established data structures like the suffix tree or the suffix array, but algorithms on compressed indexes that solve these problem are still lacking at present. Here, we show that matching statistics and maximal exact matches between two strings S1 and S2 can be computed efficiently by matching S2 backwards against a compressed index of S1.

/pdf/computing-matching-statistics-and-maximal-exact-matches-on-35v99mlzl5.pdf

Computing matching statistics and maximal exact matches on compressed full-text indexes

Searching for genes encoding microRNAs (miRNAs) is an important task in genome analysis. Because the secondary structure of miRNA (but not the sequence) is highly conserved, the genes encoding it can be determined by finding regions in a genomic DNA sequence that match the structure. It is known that algorithms using a bidirectional search on the DNA sequence for this task outperform algorithms based on unidirectional search. The data structures supporting a bidirectional search (affix trees and affix arrays), however, are rather complex and suffer from their large space consumption. Here, we present a new data structure called bidirectional wavelet index that supports bidirectional search with much less space. With this data structure, it is possible to search for candidates of RNA secondary structural patterns in large genomes, for example the complete human genome. Another important application of this data structure is short read alignment. As a second contribution, we show how bidirectional matching statistics can be computed in linear time.

Bidirectional search in a string with wavelet trees and bidirectional matching statistics

Inducing enhanced suffix arrays for string collections

Efficient algorithms for the all-pairs suffix-prefix problem and the all-pairs substring-prefix problem

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