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Approximating the Anticover of a String

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String Processing and Information Retrieval (SPIRE 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12303))

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Abstract

The k-anticover of a string S is a set of distinct k-length substrings such that every index in S is contained in one of these substrings. The existence of an anticover indicates a lack of structure in S. It was recently proven by Alzamel et al.  [2] that finding whether or not a k-anticover exists is \(\mathcal {NP}\)-Hard for \(k \ge 3\).

In this paper, we extend the definition to provide three optimization versions for the k-anticover problem. We provide efficient approximation algorithms for these problems.

This work was partially supported by ISF grant 1475/18 and BSF grant 2018141.

This work is part of the second author’s Ph.D. dissertation.

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Author information

Authors and Affiliations

  1. Department of Computer Since, Bar Ilan University, Ramat Gan, Israel

    Amihood Amir, Itai Boneh & Eitan Kondratovsky

Authors
  1. Amihood Amir
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  2. Itai Boneh
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  3. Eitan Kondratovsky
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Corresponding author

Correspondence to Itai Boneh .

Editor information

Editors and Affiliations

  1. CISE Department, University of Florida, Gainesville, FL, USA

    Christina Boucher

  2. Department of Computer Science, University of Central Florida, Orlando, FL, USA

    Sharma V. Thankachan

7 Appendix

7 Appendix

1.1 7.1 Figures

Fig. 1.
figure 1

(a) An example for MKA’s approximation ratio lower bound. (b) Simulation of MKA. (c) Simulation of MKA with least frequent heuristic

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1.2 7.2 The Experiment Results

See Table 1.

Table 1. Minimal ratio algorithm MKA (\(\alpha \)) and minimal ratio algorithm infrequent tiebreaker (\(\beta \)).
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Amir, A., Boneh, I., Kondratovsky, E. (2020). Approximating the Anticover of a String. In: Boucher, C., Thankachan, S.V. (eds) String Processing and Information Retrieval. SPIRE 2020. Lecture Notes in Computer Science(), vol 12303. Springer, Cham. https://doi.org/10.1007/978-3-030-59212-7_8

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  • DOI: https://doi.org/10.1007/978-3-030-59212-7_8

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  • Online ISBN: 978-3-030-59212-7

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