Abstract

In computational biology, -mers and edit distance are fundamental concepts. However, little is known about the metric space of all -mers equipped with the edit distance. In this work, we explore the structure of the -mer space by studying its maximal independent sets (MISs). An MIS is a sparse sketch of all -mers with nice theoretical properties, and therefore admits critical applications in clustering, indexing, hashing, and sketching large-scale sequencing data, particularly those with high error-rates. Finding an MIS is a challenging problem, as the size of a -mer space grows geometrically with respect to . We propose three algorithms for this problem. The first and the most intuitive one uses a greedy strategy. The second method implements two techniques to avoid redundant comparisons by taking advantage of the locality-property of the -mer space and the estimated bounds on the edit distance. The last algorithm avoids expensive calculations of the edit distance by translating the edit distance into the shortest path in a specifically designed graph. These algorithms are implemented and the calculated MISs of -mer spaces and their statistical properties are reported and analyzed for up to 15. Source code is freely available at https://github.com/Shao-Group/kmerspace.

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