Computing Maximal Covers for Protein Sequences

A partial cover of a string or sequence of length n , which we model as an array x = x [ 1 . . n ] , is a repeating substring u of x such that “many” positions in x lie within occurrences of u . A maximal cover u* —introduced in 2018 by Mhaskar and Smyth as optimal cover —is a partial cover that, over all partial covers u , maximizes the positions covered. Applying data structures also introduced by Mhaskar and Smyth, our software MAXCOVER for the first time enables efficient computation of u* for any x —in particular, as described here, for protein sequences of Arabidopsis, Caenorhabditis elegans, Drosophila melanogaster , and humans. In this protein context, we also compare an extended version of MAXCOVER with existing software (MUMmer's repeat-match) for the closely related task of computing non-extendible repeating substrings (a.k.a. maximal repeats ). In practice, MAXCOVER is an order-of-magnitude faster than MUMmer, with much lower space requirements, while producing more compact output that, nevertheless, yields a more exact and user-friendly specification of the repeats.