Efficient Identification of k-Closed Strings

A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. This paper addresses a new problem by extending the closed string problem to the [Formula: see text]-closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter [Formula: see text]. We address the problem of deciding whether or not a given string of length [Formula: see text] over an integer alphabet is [Formula: see text]-closed and additionally specifying the border resulting in the string being [Formula: see text]-closed. Specifically, we present an [Formula: see text]-time and [Formula: see text]-space algorithm to achieve this along with the pseudocode of an implementation and proof-of-concept experimental results.