Highly-repetitive collections of strings are increasingly being amassed by genome sequencing and genetic variation experiments, as well as by storing all versions of human-generated files, like webpages and source code. Existing indexes for locating all the exact occurrences of a pattern in a highly-repetitive string take advantage of a single measure of repetition. However, multiple, distinct measures of repetition all grow sublinearly in the length of a highly-repetitive string. In this paper we explore the practical advantages of combining data structures whose size depends on distinct measures of repetition. The main ingredient of our structures is the run-length encoded BWT (RLBWT), which takes space proportional to the number of runs in the Burrows-Wheeler transform of a string. We describe a range of practical variants that combine RLBWT with the set of boundaries of the Lempel-Ziv 77 factors of a string, which take space proportional to the number of factors. Such variants use, respectively, the RLBWT of a string and the RLBWT of its reverse, or just one RLBWT inside a bidirectional index, or just one RLBWT with support for unidirectional extraction. We also study the practical advantages of combining RLBWT with the compact directed acyclic word graph of a string, a data structure that takes space proportional to the number of one-character extensions of maximal repeats. Our approaches are easy to implement, and provide competitive tradeoffs on significant datasets. feucht. Complete inverted files for efficient text retrieval and analysis. Journal of the ACM, 34(3):578-595, 1987. 5 Timothy M Chan, Kasper Green Larsen, and Mihai Pătraşcu. Orthogonal range searching on the RAM, revisited. In Proceedings of the twenty-seventh annual symposium on computational geometry, pages 1-10. ACM, 2011. 6 Maxime Crochemore and Christophe Hancart. Automata for matching patterns. In Handbook of formal languages, pages 399-462. Springer, 1997. 7 Maxime Crochemore and Renaud Vérin. Direct construction of compact directed acyclic word graphs. A faster grammar-based self-index. In
High-throughput sequencing has revolutionised the field of biological sequence analysis. Its application has enabled researchers to address important biological questions, often for the first time. This book provides an integrated presentation of the fundamental algorithms and data structures that power modern sequence analysis workflows. The topics covered range from the foundations of biological sequence analysis (alignments and hidden Markov models), to classical index structures (k-mer indexes, suffix arrays and suffix trees), Burrows–Wheeler indexes, graph algorithms and a number of advanced omics applications. The chapters feature numerous examples, algorithm visualisations, exercises and problems, each chosen to reflect the steps of large-scale sequencing projects, including read alignment, variant calling, haplotyping, fragment assembly, alignment-free genome comparison, transcript prediction and analysis of metagenomic samples. Each biological problem is accompanied by precise formulations, providing graduate students and researchers in bioinformatics and computer science with a powerful toolkit for the emerging applications of high-throughput sequencing.
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