A simple refined DNA minimizer operator enables 2-fold faster computation

The minimizer concept is a data structure for sequence sketching. The standard canonical minimizer selects a subset of k-mers from the given DNA sequence by comparing the forward and reverse k-mers in a window simultaneously according to a predefined selection scheme. It is widely employed by sequence analysis such as read mapping and assembly. k-mer density, k-mer repetitiveness (e.g. k-mer bias), and computational efficiency are three critical measurements for minimizer selection schemes. However, there exist trade-offs between kinds of minimizer variants. Generic, effective, and efficient are always the requirements for high-performance minimizer algorithms.

We propose a simple minimizer operator as a refinement of the standard canonical minimizer. It takes only a few operations to compute. However, it can improve the k-mer repetitiveness, especially for the lexicographic order. It applies to other selection schemes of total orders (e.g. random orders). Moreover, it is computationally efficient and the density is close to that of the standard minimizer. The refined minimizer may benefit high-performance applications like binning and read mapping.

The source code of the benchmark in this work is available at the github repository https://github.com/xp3i4/mini_benchmark.