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All Instantiations of the Greedy Algorithm for the Shortest Common Superstring Problem are Equivalent

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String Processing and Information Retrieval (SPIRE 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12944))

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Abstract

In the Shortest Common Superstring problem (SCS), one needs to find the shortest superstring for a set of strings. While SCS is NP-hard and MAX-SNP-hard, the Greedy Algorithm “choose two strings with the largest overlap; merge them; repeat” achieves a constant factor approximation that is known to be at most 3.5 and conjectured to be equal to 2. The Greedy Algorithm is not deterministic, so its instantiations with different tie-breaking rules may have different approximation factors. In this paper, we show that it is not the case: all factors are equal. To prove this, we show how to transform a set of strings so that all overlaps are different whereas their ratios stay roughly the same.

The research is supported by Russian Science Foundation (18-71-10042).

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Acknowledgments

Many thanks to Alexander Kulikov for valuable discussions and proofreading the text, and the anonymous reviewers for their useful comments.

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Authors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, Russian Academy of Sciences, Saint Petersburg, Russia

    Maksim S. Nikolaev

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  1. Maksim S. Nikolaev
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Editors and Affiliations

  1. Université de Rouen Normandie, Mont-St-Aignan, France

    Thierry Lecroq

  2. CNRS, CRIStAL, Villeneuve d'Ascq, France

    Hélène Touzet

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Nikolaev, M.S. (2021). All Instantiations of the Greedy Algorithm for the Shortest Common Superstring Problem are Equivalent. In: Lecroq, T., Touzet, H. (eds) String Processing and Information Retrieval. SPIRE 2021. Lecture Notes in Computer Science(), vol 12944. Springer, Cham. https://doi.org/10.1007/978-3-030-86692-1_6

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  • DOI: https://doi.org/10.1007/978-3-030-86692-1_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86691-4

  • Online ISBN: 978-3-030-86692-1

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