The k-mappability problem revisited

Abstract

The k-mappability problem has two integers parameters m and k. For every subword of size m in a text S, we wish to report the number of indices in S in which the word occurs with at most k mismatches.The problem was lately tackled by Alzamel et al. [1]. For a text with constant alphabet Σ and k ∈ O(1), they present an algorithm with linear space and O(n log k+1 n) time. For the case in which k = 1 and a constant size alphabet, a faster algorithm with linear space and O(n log(n) log log(n)) time was presented in [2].In this work, we enhance the techniques of [2] to obtain an algorithm with linear space and O(n log(n)) time for k = 1. Our algorithm removes the constraint of the alphabet being of constant size. We also present linear algorithms for the case of k = 1, |Σ| ∈ O(1) and m = Ω( √ n).