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Dynamic Distance Hereditary Graphs Using Split Decomposition

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Algorithms and Computation (ISAAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4835))

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Abstract

The problem of maintaining a representation of a dynamic graph as long as a certain property is satisfied has recently been considered for a number of properties. This paper presents an optimal algorithm for this problem on vertex-dynamic connected distance hereditary graphs: both vertex insertion and deletion have complexity O(d), where d is the degree of the vertex involved in the modification. Our vertex-dynamic algorithm is competitive with the existing linear time recognition algorithms of distance hereditary graphs, and is also simpler. Besides, we get a constant time edge-dynamic recognition algorithm. To achieve this, we revisit the split decomposition by introducing graph-labelled trees. Doing so, we are also able to derive an intersection model for distance hereditary graphs, which answers an open problem.

Research supported by the French ANR project “Graph Decompositions and Algorithms (GRAAL)”.

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Authors and Affiliations

  1. CNRS - LIRMM, Université de Montpellier 2, France

    Emeric Gioan & Christophe Paul

Authors
  1. Emeric Gioan
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  2. Christophe Paul
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Editor information

Takeshi Tokuyama

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Gioan, E., Paul, C. (2007). Dynamic Distance Hereditary Graphs Using Split Decomposition. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_6

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  • DOI: https://doi.org/10.1007/978-3-540-77120-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77118-0

  • Online ISBN: 978-3-540-77120-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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