MOTIVATION: Large-scale sequencing projects have confirmed the hypothesis that eukaryotic DNA is rich in repetitions whose functional role needs to be elucidated. In particular, tandem repeats (TRs) (i.e. short, almost identical sequences that lie adjacent to each other) have been associated to many cellular processes and, indeed, are also involved in several genetic disorders. The need of comprehensive lists of TRs for association studies and the absence of a computational model able to capture their variability have revived research on discovery algorithms. RESULTS: Building upon the idea that sequence similarities can be easily displayed using graphical methods, we formalized the structure that TRs induce in dot-plot matrices where a sequence is compared with itself. Leveraging on the observation that a compact representation of these matrices can be built and searched in linear time, we developed Dot2dot: an accurate algorithm fast enough to be suitable for whole-genome discovery of TRs. Experiments on five manually curated collections of TRs have shown that Dot2dot is more accurate than other established methods, and completes the analysis of the biggest known reference genome in about one day on a standard PC. AVAILABILITY AND IMPLEMENTATION: Source code and datasets are freely available upon paper acceptance at the URL: https://github.com/Gege7177/Dot2dot. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Single nucleotide polymorphism (SNP) is the most frequent form of DNA variation. The set of SNP's present in a chromosome (called the haplotype) is of interest in a wide area of applications in molecular biology and biomedicine, including diagnostic and medical therapy. In this paper we propose a new heuristic method for the problem of haplotype reconstruction for (portions of) a pair of homologous human chromosomes from a single individual (SIH). The problem is well known in literature and exact algorithms have been proposed for the case when no (or few) gaps are allowed in the input fragments. These algorithms, though exact and of polynomial complexity, are slow in practice. When gaps are considered no exact method of polynomial complexity is known. The problem is also hard to approximate with guarantees. Therefore fast heuristics have been proposed. In this paper we describe SpeedHap, a new heuristic method that is able to tackle the case of many gapped fragments and retains its effectiveness even when the input fragments have high rate of reading errors (up to 20%) and low coverage (as low as 3). We test SpeedHap on real data from the HapMap Project.