On the complexity of finding common approximate substrings

• Published in: Theoretical computer science Vol. 306; no. 1-3; pp. 407 - 430
• Main Authors: Evans, Patricia A., Smith, Andrew D., Wareham, H.Todd
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 05-09-2003; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Common approximate substring; Computer science; control theory; systems; Exact sciences and technology; Parameterized complexity; Pattern matching; Pattern recognition. Digital image processing. Computational geometry; Common approximate substring; Parameterized complexity; Pattern matching; Hamming distance; Pattern recognition; Approximate solution; Concordance; Parametrized complexity; Complexity
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/S0304-3975(03)00320-7

Problems associated with finding strings that are within a specified Hamming distance of a given set of strings occur in several disciplines. In this paper, we use techniques from parameterized complexity to assess non-polynomial time algorithmic options and complexity for the COMMON APPROXIMATE SUBSTRING (CAS) problem. Our analyses indicate under which parameter restrictions useful algorithms are possible, and include both class membership and parameterized reductions to prove class hardness. In order to achieve fixed-parameter tractability, either a fixed string length or both a fixed size alphabet and fixed substring length are sufficient. Fixing either the string length or the alphabet size and Hamming distance is shown to be necessary, unless W[1]=FPT. An assortment of parameterized class membership and hardness results cover all other parameterized variants, showing in particular the effect of fixing the number of strings.