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Scaffolding Problems Revisited: Complexity, Approximation and Fixed Parameter Tractable Algorithms, and Some Special Cases

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Abstract

This paper is devoted to new results about the scaffolding problem, an integral problem of genome inference in bioinformatics. The problem consists in finding a collection of disjoint cycles and paths covering a particular graph called the “scaffold graph”. We examine the difficulty and the approximability of the scaffolding problem in special classes of graphs, either close to trees, or very dense. We propose negative and positive results, exploring the frontier between difficulty and tractability of computing and/or approximating a solution to the problem. Also, we explore a new direction through related problems consisting in finding a family of edges having a strong effect on solution weight.

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Notes

  1. The ETH states that there is a constant \(c >1\) such that n-variable 3SAT cannot be solved in \(O(c^n)\) time.

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Acknowledgements

This work was supported by the Institut de Biologie Computationnelle (http://www.ibc-montpellier.fr/) (ANR Projet Investissements d’Avenir en bioinformatique IBC).

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Authors and Affiliations

  1. LIGM - CNRS UMR 8049, Marne-La-Vallée, France

    Mathias Weller

  2. LIRMM - CNRS UMR 5506, Montpellier, France

    Annie Chateau & Rodolphe Giroudeau

  3. School of Computing, University of Portsmouth, UK

    Clément Dallard

Authors
  1. Mathias Weller
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  2. Annie Chateau
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  3. Clément Dallard
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  4. Rodolphe Giroudeau
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Correspondence to Annie Chateau.

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Weller, M., Chateau, A., Dallard, C. et al. Scaffolding Problems Revisited: Complexity, Approximation and Fixed Parameter Tractable Algorithms, and Some Special Cases. Algorithmica 80, 1771–1803 (2018). https://doi.org/10.1007/s00453-018-0405-x

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  • DOI: https://doi.org/10.1007/s00453-018-0405-x

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