@article{494a1cbddd84401e94ac745ec58e638e, title = "Faster algorithms for 1-mappability of a sequence", abstract = "In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y. We focus here on the version of the problem where k=1. There exists an algorithm to solve this problem for k=1 requiring time O(mnlogn/loglogn) using space O(n). Here we present two new algorithms that require worst-case time O(mn) and O(nlognloglogn), respectively, and space O(n), thus greatly improving the previous result. Moreover, we present another algorithm that requires average-case time and space O(n) for integer alphabets of size σ if m=Ω(log σn). Notably, we show that this algorithm is generalizable for arbitrary k, requiring average-case time O(kn) and space O(n) if m=Ω(klog σn), assuming that the letters are independent and uniformly distributed random variables. Finally, we provide an experimental evaluation of our average-case algorithm demonstrating its competitiveness to the state-of-the-art implementation. ", keywords = "Algorithms on strings, Hamming distance, Sequence mappability", author = "Mai Alzamel and Panagiotis Charalampopoulos and Iliopoulos, {Costas S.} and Pissis, {Solon P.} and Jakub Radoszewski and Wing-Kin Sung", year = "2019", month = may, day = "23", doi = "10.1016/j.tcs.2019.04.026", language = "English", journal = "Theoretical Computer Science", issn = "0304-3975", publisher = "Elsevier", }