Abstract
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 \(\ell \) containing 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.
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The research leading to these results has received funding from the Government of the Russian Federation (Grant 14.Z50.31.0030) and the Grant of the President of Russian Federation (MK-6550.2015.1). A preliminary version of the paper appeared in the proceedings of CPM 2015.
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Bliznets, I., Fomin, F.V., Golovach, P.A. et al. Parameterized Complexity of Superstring Problems. Algorithmica 79, 798–813 (2017). https://doi.org/10.1007/s00453-016-0193-0
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DOI: https://doi.org/10.1007/s00453-016-0193-0