# Global Repeat Map (GRM) Application: Finding All DNA Tandem Repeat Units
## 1 Introduction
Statistical string-matching algorithms have problems with: (i) repeats containing sizeable substitutions and/or insertions/deletions, (ii) repeats having very large repeat units (above 2 kb), (iii) several overlapping possible repeat structures, and (iv) excessive running time. Signal-processing algorithms have problems with (i) numerical artifacts, (ii) the poor resolution of spectral analyses and (iii) significant background noise that masks information. In general, because of the approximate, polymorphic and copy number variant nature of repeat units, the identification of TRs is a very complex problem, and different algorithms exhibit different degrees of robustness for various types of repeats [50]. Accordingly, in order to detect as many different types of polymorphic repeats as possible, some algorithms introduce an arbitrarily threshold, as well as user-defined parameters, which influence the results. In this way, depending on the choice of parameters/thresholds, the algorithms identify only one part of the TRs (for example, only small ones, or only approximately regular ones) and ignore the others. Therefore, it is clear that there still remains a high potential for improving the efficiency of different methods and algorithms for TR detection. Here, we present our new GRM algorithm, and accompanying GRM application, which is designed to overcome all of the above-mentioned limitations: (i) it does not require any prior knowledge of the sequence structure (ii) it does not use any arbitrary or user-defined parameters/thresholds; (iii) it is robust to substitutions and insertions/deletions, as well as to the various complexities of the sequence pattern; (iv) it is applicable to all repeat units, from very small to very large, as large as tens of kilobasepairs; (v) it is very fast (detection of all the TRs in an average size (50 Mbps) chromosome takes less than a minute on a personal computer). Our new GRM algorithm incorporates the main ideas presented in [50; 52; 53], with significant modifications and extensions to achieve the goal of the detection and extraction of all the TRs in one step. The main advantage of the new algorithm is that, unlike the previous one, it is fully automated and does not require any prior knowledge of the sequence, or any knowledge of GRM diagram analysis. The user of the GRM application simply loads the DNA sequence and gets a report of all the TRs in a given sequence, their positions, TR copy numbers, TR lengths and the TR sequences broken down into repetitive units. Science is entering into a new era of genomics, with high-resolution maps based on long reads, where centromeric regions are accurately represented [54]. Now, in centromeric regions, canonical HOR units, many structural variant types with a high variation in relative frequency, have become accessible and prompted the development of new software programs to precisely find or characterize TR using DNA-sequencing data. Global Repeat Map is just such a novel software, which enables the precise identification of complex repeats [55; 56]. Complete sequencing requires highly sophisticated software for its analysis. The remainder of this paper is organized as follows. In Materials and Methods, we present a new GRM algorithm. In Results, we present the usage of the GRM application for the entire sequence of human, chimpanzee and mouse chromosome 19. Finally, in Discussion, we describe directions for future research and development and the possible improvements of the application.