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arXiv · 1502.01461

Parameterized Complexity of Superstring Problems

Ivan Bliznets·Fedor V. Fomin·Petr A. Golovach·Nikolay Karpov·Alexander S. Kulikov·Saket Saurabh
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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 $2^{O(k)} \operatorname{poly}(n)$ finds a superstring of length at most $\ell$ containing at least $k$ strings of $S$. We complement this by the 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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Ivan Bliznets, Fedor V. Fomin, Petr A. Golovach, Nikolay Karpov, Alexander S. Kulikov, Saket Saurabh. 2015-02-05. Parameterized Complexity of Superstring Problems. https://arxiv.org/abs/1502.01461

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