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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. [ABSTRACT FROM AUTHOR]