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Finding the Anticover of a String

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

Mai Alzamel, Alessio Conte, Shuhei Denzumi, Roberto Grossi, Costas S. Iliopoulos, Kazuhiro Kurita, Kunihiro Wasa

Original languageEnglish
Title of host publication31st Annual Symposium on Combinatorial Pattern Matching, CPM 2020
EditorsInge Li Gortz, Oren Weimann
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771498
Published1 Jun 2020
Event31st Annual Symposium on Combinatorial Pattern Matching, CPM 2020 - Copenhagen, Denmark
Duration: 17 Jun 202019 Jun 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference31st Annual Symposium on Combinatorial Pattern Matching, CPM 2020

King's Authors


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. 2012 ACM Subject Classification Mathematics of computing ! Combinatorics on words.

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