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SOFSEM 2020: SOFSEM 2020: Theory and Practice of Computer Science pp 76–87Cite as

Approximating Shortest Connected Graph Transformation for Trees

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12011))

Abstract

Let G, H be two connected graphs with the same degree sequence. The aim of this paper is to find a transformation from G to H via a sequence of flips maintaining connectivity. A flip of G is an operation consisting in replacing two existing edges uv, xy of G by ux and vy.

Taylor showed that there always exists a sequence of flips that transforms G into H maintaining connectivity. Bousquet and Mary proved that there exists a 4-approximation algorithm of a shortest transformation. In this paper, we show that there exists a 2.5-approximation algorithm running in polynomial time. We also discuss the tightness of the lower bound and show that, in order to drastically improve the approximation ratio, we need to improve the best known lower bounds.

This work was supported by ANR project GrR (ANR-18-CE40-0032).

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Notes

  1. 1.

    In the case of multigraphs, we simply decrease by one the multiplicities of ab and cd and increase by one the ones of ac and bd.

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Author information

Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, Laboratoire G-SCOP, Grenoble-INP, Grenoble, France

    Nicolas Bousquet

  2. LIRIS, Université Claude Bernard, Lyon, France

    Alice Joffard

Authors
  1. Nicolas Bousquet
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  2. Alice Joffard
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Corresponding author

Correspondence to Alice Joffard .

Editor information

Editors and Affiliations

  1. University of Macedonia, Thessaloniki, Greece

    Alexander Chatzigeorgiou

  2. University of Bergamo, Bergamo, Italy

    Riccardo Dondi

  3. Cyprus University of Technology, Limassol, Cyprus

    Herodotos Herodotou

  4. Carnegie Mellon University Qatar, Doha, Qatar

    Christos Kapoutsis

  5. Open University of Cyprus, Nicosia, Cyprus

    Yannis Manolopoulos

  6. University of Cyprus, Nicosia, Cyprus

    George A. Papadopoulos

  7. Paris Dauphine University, Paris, France

    Florian Sikora

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Bousquet, N., Joffard, A. (2020). Approximating Shortest Connected Graph Transformation for Trees. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-38919-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38918-5

  • Online ISBN: 978-3-030-38919-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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