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. In this paper, we extend this definition to k-closed strings, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter k. We then address the problem of identifying 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 O(kn)O(kn) -time and O(n)O(n) -space algorithm to achieve this along with the pseudocode of an implementation.
|Title of host publication||Engineering Applications of Neural Networks: 18th International Conference, EANN 2017, Athens, Greece, August 25--27, 2017, Proceedings|
|Editors||Giacomo Boracchi, Lazaros Iliadis, Chrisina Jayne, Aristidis Likas|
|Place of Publication||Cham|
|Publisher||Springer International Publishing Switzerland|
|Number of pages||13|
|Publication status||E-pub ahead of print - 2 Aug 2017|