String Matching with Involutions

In this note we propose a novel algorithm for locating in a text T every occurrence of a strings that can be obtained from a given pattern P by successively applying antimorphic involutions on some of its factors. When the factors on which these involutions are applied overlap, a linear time algorithm is obtained. When we apply the involutions to non-overlapping factors we obtain an algorithm running in O(|T ||P |) time and O(|P |) space, in the worst case. We also improve the latter algorithm to achieve linear average running time, when the alphabet of the pattern is large enough.