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On Maximum Common Subgraph Problems in Series-Parallel Graphs

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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  • International Workshop on Combinatorial Algorithms

Abstract

The complexity of the maximum common connected subgraph problem in partial k-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial 2-trees. On the contrary, the problem is known to be NP-hard in vertex-labeled partial 11-trees of bounded degree. We consider series-parallel graphs, i.e., partial 2-trees. We show that the problem remains NP-hard in biconnected series-parallel graphs with all but one vertex of degree bounded by three. A positive complexity result is presented for a related problem of high practical relevance which asks for a maximum common connected subgraph that preserves blocks and bridges of the input graphs. We present a polynomial time algorithm for this problem in series-parallel graphs, which utilizes a combination of BC- and SP-tree data structures to decompose both graphs.

This work was supported by the German Research Foundation (DFG), priority programme “Algorithms for Big Data” (SPP 1736).

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Notes

  1. 1.

    We call vertices of SP- and BC-trees nodes and vertices of the input graphs vertices.

  2. 2.

    If an instance of NMwTS does not allow the construction of \(D^{v}_{w}\), all values are multiplied by 3.

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Authors and Affiliations

  1. Department of Computer Science, Technische Universität Dortmund, Dortmund, Germany

    Nils Kriege, Florian Kurpicz & Petra Mutzel

Authors
  1. Nils Kriege
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  2. Florian Kurpicz
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  3. Petra Mutzel
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Corresponding author

Correspondence to Florian Kurpicz .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Kriege, N., Kurpicz, F., Mutzel, P. (2015). On Maximum Common Subgraph Problems in Series-Parallel Graphs. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_18

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_18

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  • Online ISBN: 978-3-319-19315-1

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