A practical index for approximate dictionary matching with few mismatches

Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a surprisingly simple solution called a split index, which is based on the Dirichlet principle, for matching a keyword with few mismatches, and experimentally show that it offers competitive space-time tradeoffs. Our implementation in the C++ language is focused mostly on data compaction, which is beneficial for the search speed (e.g., by being cache friendly). We compare our solution with other algorithms and we show that it performs better for the Hamming distance. Query times in the order of 1 microsecond were reported for one mismatch for the dictionary size of a few megabytes on a medium-end PC. We also demonstrate that a basic compression technique consisting in $q$-gram substitution can significantly reduce the index size (up to 50% of the input text size for the DNA), while still keeping the query time relatively low

Average-Case Optimal Approximate Circular String Matching

Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that are at a distance at most k from x or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the edit distance model with optimal average-case search time O(n(k + log m)/m). Optimal average-case search time can also be achieved by the algorithms for multiple approximate string matching (Fredriksson and Navarro, 2004) using x and its rotations as the set of multiple patterns. Here we reduce the preprocessing time and space requirements compared to that approach

Indexing large genome collections on a PC

Motivation: The availability of thousands of invidual genomes of one species should boost rapid progress in personalized medicine or understanding of the interaction between genotype and phenotype, to name a few applications. A key operation useful in such analyses is aligning sequencing reads against a collection of genomes, which is costly with the use of existing algorithms due to their large memory requirements. Results: We present MuGI, Multiple Genome Index, which reports all occurrences of a given pattern, in exact and approximate matching model, against a collection of thousand(s) genomes. Its unique feature is the small index size fitting in a standard computer with 16--32\,GB, or even 8\,GB, of RAM, for the 1000GP collection of 1092 diploid human genomes. The solution is also fast. For example, the exact matching queries are handled in average time of 39\,$\mu$s and with up to 3 mismatches in 373\,$\mu$s on the test PC with the index size of 13.4\,GB. For a smaller index, occupying 7.4\,GB in memory, the respective times grow to 76\,$\mu$s and 917\,$\mu$s. Availability: Software and Suuplementary material: \url{http://sun.aei.polsl.pl/mugi}

Analysis of Min-Hashing for Variant Tolerant DNA Read Mapping

DNA read mapping has become a ubiquitous task in bioinformatics. New technologies provide ever longer DNA reads (several thousand basepairs), although at comparatively high error rates (up to 15%), and the reference genome is increasingly not considered as a simple string over ACGT anymore, but as a complex object containing known genetic variants in the population. Conventional indexes based on exact seed matches, in particular the suffix array based FM index, struggle with these changing conditions, so other methods are being considered, and one such alternative is locality sensitive hashing. Here we examine the question whether including single nucleotide polymorphisms (SNPs) in a min-hashing index is beneficial. The answer depends on the population frequency of the SNP, and we analyze several models (from simple to complex) that provide precise answers to this question under various assumptions. Our results also provide sensitivity and specificity values for min-hashing based read mappers and may be used to understand dependencies between the parameters of such methods. We hope that this article will provide a theoretical foundation for a new generation of read mappers