PLA-index: A k-mer Index Exploiting Rank Curve Linearity

Given a sorted list of k-mers S, the rank curve of S is the function mapping a k-mer from the k-mer universe to the location in S where it either first appears or would be inserted. An exciting recent development is the observation that, for certain datasets, the rank curve is predictable and can be exploited to create small search indices. In this paper, we develop a novel search index that first estimates a k-mer's rank using a piece-wise linear approximation of the rank curve and then does a local search to determine the precise location of the k-mer in the list. We combine ideas from previous approaches and supplement them with an innovative data representation strategy that substantially reduces space usage. Our PLA-index uses an order of magnitude less space than Sapling and uses less than half the space of the PGM-index, for roughly the same query time. For example, using only 9 MiB of memory, it can narrow down the position of k-mer in the suffix array of the human genome to within 255 positions. Furthermore, we demonstrate the potential of our approach to impact a variety of downstream applications. First, the PLA-index halves the time of binary search on the suffix array of the human genome. Second, the PLA-index reduces the space of a direct-access lookup table by 76 percent, without increasing the run time. Third, we plug the PLA-index into a state-of-the-art read aligner Strobealign and replace a 2 GiB component with a PLA-index of size 1.5 MiB, without significantly effecting runtime. The software and reproducibility information is freely available at https://github.com/medvedevgroup/pla-index.