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 k-closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter k. We address the problem of deciding whether or not a given string of length n over an integer alphabet is k-closed and additionally specifying the border resulting in the string being k-closed. Specifically, we present an (kn)-time and (n)-space algorithm to achieve this along with the pseudocode of an implementation and proof-of-concept experimental results.

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