The k-mappability problem revisited
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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. For a text with constant alphabet Σ and k ∈ O(1), they present an algorithm with linear space and O(nlog^k+1n) time. For the case in which k = 1 and a constant size alphabet, a faster algorithm with linear space and O(nlog(n)loglog(n)) time was presented in a 2020 paper by Alzamel et al. In this work, we enhance the techniques of Alzamel et al.'s 2020 paper 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)).
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