Parameterized Intractability of Motif Search Problems

Michael R. Fellows; Jens Gramm; Rolf Niedermeier

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Parameterized Intractability of Motif Search Problems

Michael R. Fellows·Jens Gramm·Rolf Niedermeier

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Abstract

We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k)\cdot n^{c}) for any function f of k and constant c independent of k. The problem can therefore be expected to be intractable, in any practical sense, for k>=3. Our result supports the intuition that Closest Substring is computationally much harder than the special case of Closest String, although both problems are NP-complete. We also prove W[1]-hardness for other parameterizations in the case of unbounded alphabet size. Our W[1]-hardness result for Closest Substring generalizes to Consensus Patterns, a problem of similar significance in computational biology.

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Michael R. Fellows, Jens Gramm, Rolf Niedermeier. 2002-05-21. Parameterized Intractability of Motif Search Problems. https://arxiv.org/abs/cs/0205056

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