Efficient computation of sequence mappability

Sequence mappability is an important task in genome resequencing. In the (k, m)-mappability problem, for a given sequence T of length n, the goal is to compute a table whose ith entry is the number of indices j≠ i such that the length-m substrings of T starting at positions i and j have at most k mismatches. Previous works on this problem focused on heuristics computing a rough approximation of the result or on the case of k= 1. We present several efficient algorithms for the general case of the problem. Our main result is an algorithm that, for k= O(1) , works in O(n) space and, with high probability, in O(n· min { mk, log kn}) time. Our algorithm requires a careful adaptation of the k-errata trees of Cole et al. [STOC 2004] to avoid multiple counting of pairs of substrings. Our technique can also be applied to solve the all-pairs Hamming distance problem introduced by Crochemore et al. [WABI 2017]. We further develop O(n2) -time algorithms to compute all (k, m)-mappability tables for a fixed m and all k∈ { 0 , … , m} or a fixed k and all m∈ { k, … , n}. Finally, we show that, for k, m= Θ (log n) , the (k, m)-mappability problem cannot be solved in strongly subquadratic time unless the Strong Exponential Time Hypothesis fails. This is an improved and extended version of a paper presented at SPIRE 2018

Fast and compact hamming distance index

Searching for similar objects in a collection is a core task of many applications in databases, pattern recognition, and information retrieval. As there exist similarity-preserving hash functions like SimHash, indexing these objects reduces to the solution of the Approximate Dictionary Queries problem. In this problem we have to index a collection of fixed-sized keys to efficiently retrieve all the keys which are at a Hamming distance at most κ from a query key. In this paper we propose new solutions for the approximate dictionary queries problem. These solutions combine the use of succinct data structures with an efficient representation of the keys to significantly reduce the space usage of the state-of-the-art solutions without introducing any time penalty. Finally, by exploiting triangle inequality, we can also significantly speed up the query time of the existing solutions