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Regular version of the site

Article

Parameterized Complexity of Superstring Problems

Algorithmica. 2017. Vol. 79. No. 3. P. 798-813.
Bliznets Ivan, Fomin F., Golovach P., Karpov N., Kulikov A. S., Saurabh S.

In the Shortest Superstring problem we are given a set of strings S=\{s_1, \ldots , s_n\} and integer \ell and the question is to decide whether there is a superstring s of length at most \ellcontaining all strings of S as substrings. We obtain several parameterized algorithms and complexity results for this problem. In particular, we give an algorithm which in time 2^{\mathcal {O}(k)} {\text {poly}}(n) finds a superstring of length at most \ell containing at least k strings of S. We complement this by a lower bound showing that such a parameterization does not admit a polynomial kernel up to some complexity assumption. We also obtain several results about “below guaranteed values” parameterization of the problem. We show that parameterization by compression admits a polynomial kernel while parameterization “below matching” is hard.