Deterministic Techniques for K-Mer Frequency Counting

Snippets or sub-strings taken from longer sequences of genetic material such as DNA or RNA are called ‘k-mers’, where the ‘k’ is a number that represents the length of the substring. As an example, a ’10-mer’ would refer to sub-strings of length 10 taken from a longer genetic sequence. K-mers are important objects used in genomics in applications such as genome assembly, sequence alignment, metagenomics, sequence similarity search, error correction among other use cases, and as such are a focal point of research in the field of bioinformatics. Two important areas of research are K-mer frequency counting and K-mer searching/matching. The former is the focus of this paper. K-mer frequency counting aims to count the number of occurrences of all k-mers in a given sequence as well as find other related information such as the most frequently occurring k-mer and its count in the given sequence. The importance of k-mer frequency counting is expanded upon in further sections of this paper. Current generation k-mer frequency counting software use a mix of probabilistic and deterministic techniques and are constructed using basic algorithms such as Hashing, Suffix Arrays/Tries, Bloom Filter, and Sorting. This paper examines these basic algorithms in the context of k-mer frequency counting and compares some of the prominent software used for k-mer frequency counting. Two different approaches that utilise these basic algorithms are proposed. These approaches are not meant as replacements to the aforementioned software but rather as intermediate techniques that can be made use of by newer algorithms and software. It must be noted that the focus of this paper lies solely on deterministic techniques as it is the view of the authors that current generation probabilistic techniques will be superseded by Machine Learning techniques. In such a scenario it only becomes more important that deterministic techniques that are guaranteed to deliver results with 100% accuracy are researched.