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Background  Measuring sequence similarity is central for many problems in bioinformatics. In several contexts alignment-free techniques based on exact occurrences of substrings are faster, but also less accurate, than alignment-based approaches. Recently, several studies attempted to bridge the accuracy gap with the introduction of approximate matches in the definition of composition-based similarity measures.    Results  In this work we present  MissMax , an exact algorithm for the computation of the longest common substring with mismatches between each suffix of a sequence  x  and a sequence  y . This collection of statistics is useful for the computation of two similarity measures: the longest and the average common substring with  k  mismatches. As a further contribution we provide a “relaxed” version of MissMax that does not guarantee the exact solution, but it is faster in practice and still very precise.

MissMax: alignment-free sequence comparison with mismatches through filtering and heuristics