Finding similar regions in many strings
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
Mathematical Methods for DNA Sequences
Mathematical Methods for DNA Sequences
Spelling Approximate Repeated or Common Motifs Using a Suffix Tree
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
On the Parameterized Intractability of CLOSEST SUBSTRINGsize and Related Problems
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On the complexity of finding common approximate substrings
Theoretical Computer Science
Parameterized Complexity
More efficient algorithms for closest string and substring problems
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
More Efficient Algorithms for Closest String and Substring Problems
SIAM Journal on Computing
Finding compact structural motifs
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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The Closest Substring Problem is one of the most important problems in the field of computational biology. It is stated as follows: given a set of t sequences s1, s2,...,st over an alphabet Σ, and two integers k,d with d ≤ k, can one find a string s of length k and, for all i=1,2,...,t, substrings oi of si, all of length k, such that d(s,oi) ≤ d (for all i= 1,2,...,t)? (here, d(.,.) represents the Hamming distance). Closest Substring was shown to be NP-hard (Proceedings of 10th SODA, 1999, pp. 633-642) and W[1]-hard with respect to the number t of input sequences (Proceedings of STACS'02, Lecture Notes in Computer Science, Vol. 2285, 2002, pp. 262-273); recently, an important number of results concerning the parameterized computational complexity of Closest Substring has been added in Evans et al. (Theoret. Comput. Sci. 306 (1-3) (2003) 407). In this paper we introduce and analyze two variants of the Closest Substring Problem, obtained by imposing restrictions on the pairwise distances between the substrings oi: • the bounded Hamming distance constraint asks that d(oi,oj) ≤ p, for all i,j ∈ {1,2,...,t} (where p i≤ij≤t d(oi,oj) ≤ P (where P dt(t - 1) is a given constant) and yields the problem called SCCS. We motivate the introduction of these problems, and we show that while SCCS is very close to Closest Substring, BCCS is a non-trivial restriction of Closest Substring more suitable to use in certain practical applications. We then concentrate on BCCS and show that all the hardness results available for Closest Substring remain valid for BCCS even when the parameter p is restricted to a certain range.