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Approximating Shortest Connected Graph Transformation for Trees

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SOFSEM 2020: Theory and Practice of Computer Science (SOFSEM 2020)

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

Abstract

Let GH 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 uvxy 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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Correspondence to Alice Joffard .

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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

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