This paper is concerned with practical implementations of approximate string dictionaries that allow edit errors. In this problem, we have as input a dictionary D of d strings of total length n over an alphabet of size σ . Given a bound k and a pattern x of length m, a query has to return all the strings of the dictionary which are at edit distance at most k from x, where the edit distance between two strings x and y is defined as the minimum-cost sequence of edit operations that transform x into y. The cost of a sequence of operations is defined as the sum of the costs of the operations involved in the sequence. In this paper, we assume that each of these operations has unit cost and consider only three operations: deletion of one character, insertion of one character and substitution of a character by another. We present a practical implementation of the data structure we recently proposed and which works only for one error. We extend the scheme to 2 ≤ k < m.Our implementation has many desirable properties: it has a very fast and space-efficient building algorithm. The dictionary data structure is compact and has fast and robust query time. Finally our data structure is simple to implement as it only uses basic techniques from the literature, mainly hashing (linear probing and hash signatures) and succinct data structures (bitvectors supporting rank queries).

Motivation Alternative splicing is a ubiquitous process in eukaryotes that allows distinct transcripts to be produced from the same gene. Yet, the study of transcript evolution within a gene family is still in its infancy. One prerequisite for this study is the availability of methods to compare sets of transcripts while accounting for their splicing structure. In this context, we generalize the concept of pairwise spliced alignments to multiple spliced alignments (MSpAs). MSpAs have several important purposes in addition to empowering the study of the evolution of transcripts. For instance, it is a key to improving the prediction of gene models, which is important to solve the growing problem of genome annotation. Despite its essentialness, a formal definition of the concept and methods to compute MSpAs are still lacking. Results We introduce the MSpA problem and the SplicedFamAlignMulti (SFAM) method, to compute the MSpA of a gene family. Like most multiple sequence alignment (MSA) methods that are generally greedy heuristic methods assembling pairwise alignments, SFAM combines all pairwise spliced alignments of coding DNA sequences (CDSs) and gene sequences of a gene family into an MSpA. It produces a single structure that represents the super-structure and models of the gene family. Using real vertebrate and simulated gene family data, we illustrate the utility of SFAM for computing accurate gene family super-structures, MSAs, inferring splicing orthologous groups, and improving gene-model annotations. Availability The supporting data and implementation of SFAM are freely available at https://github.com/UdeS-CoBIUS/SpliceFamAlignMulti.

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