Parameterized Complexity of Superstring Problems

Abstract

In the Shortest Superstring problem we are given a set of strings S = {s 1 , . . . , s n } and integer ℓ and the question is to decide whether there is a superstring s of length at most ℓ 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) poly(n) finds a superstring of length at most ℓ 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. * The research leading to these results has received funding from the Government of the Russian Federation (grant 14.Z50.31.0030).