Sequence mappability is an important task in genome re-sequencing. In the (k, m)-mappability problem, for a given sequence T of length n, our goal is to compute a table whose ith entry is the number of indices j≠i such that length-m substrings of T starting at positions i and j have at most k mismatches. Previous works on this problem focused on heuristic approaches to compute 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 works in O(n min {mk,log k+1 n}) time and O(n) space for k=O(1). It requires a careful adaptation of the technique of Cole et al. [STOC 2004] to avoid multiple counting of pairs of substrings. We also show O(n2) -time algorithms to compute all results for a fixed m and all k=0,…,m or a fixed k and all m=k,…,n-1. Finally we show that the (k, m)-mappability problem cannot be solved in strongly subquadratic time for k,m = Θ (log n) unless the Strong Exponential Time Hypothesis fails.
CITATION STYLE
Alzamel, M., Charalampopoulos, P., Iliopoulos, C. S., Kociumaka, T., Pissis, S. P., Radoszewski, J., & Straszyński, J. (2018). Efficient computation of sequence mappability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11147 LNCS, pp. 12–26). Springer Verlag. https://doi.org/10.1007/978-3-030-00479-8_2
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