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International Conference on Theory and Applications of Models of Computation

TAMC 2010: Theory and Applications of Models of Computation pp 175–186Cite as

An \({\mathcal{O}}(n^2)\)-time Algorithm for the Minimal Interval Completion Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6108))

Abstract

The minimal interval completion problem consists in adding edges to an arbitrary graph so that the resulting graph is an interval graph; the objective is to add an inclusion minimal set of edges, which means that no proper subset of the added edges can result in an interval graph when added to the original graph. We give an \({\mathcal{O}}(n^2)\)-time algorithm to obtain a minimal interval completion of an arbitrary graph. This improves the previous O(nm) time bound for the problem and lower this bound for the first time below the best known bound for minimal chordal completion.

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Author information

Authors and Affiliations

  1. LIP6, Université Paris 6,  

    Christophe Crespelle

  2. LIFO, Université d’Orleans, BP 6759, F-45067, Orleans Cedex 2, France

    Ioan Todinca

Authors
  1. Christophe Crespelle
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  2. Ioan Todinca
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Editor information

Editors and Affiliations

  1. Charles University, Malostranske nam 25, 11800, Praha 1, Czech Republic

    Jan Kratochvíl , Jiří Fiala  & Petr Kolman ,  & 

  2. State Key Lab. of Computer Science, Institute of Software,, Chinese Academy of Sciences, 100190, Beijing, P.R. China

    Angsheng Li

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Crespelle, C., Todinca, I. (2010). An \({\mathcal{O}}(n^2)\)-time Algorithm for the Minimal Interval Completion Problem. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_17

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  • DOI: https://doi.org/10.1007/978-3-642-13562-0_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13561-3

  • Online ISBN: 978-3-642-13562-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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