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Finding the Anticover of a String

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Abstract

A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k ≥ 3. We also show that the problem admits a polynomial-time solution for k = 2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O*(min{3 n−k 3 , (k(k+1) 2) n k+1}) time using polynomial space.
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Dates and versions

hal-02957658 , version 1 (05-10-2020)

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Cite

Mai Alzamel, Alessio Conte, Shuhei Denzumi, Roberto Grossi, Costas S Iliopoulos, et al.. Finding the Anticover of a String. CPM 2020 - 31st Annual Symposium on Combinatorial Pattern Matching, Jun 2020, Copenhagen, Denmark. pp.1-11, ⟨10.4230/LIPIcs.CPM.2020.2⟩. ⟨hal-02957658⟩

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