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Two-Layer Planarization Parameterized by Feedback Edge Set

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Theory and Applications of Models of Computation (TAMC 2010)

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

Abstract

Given an undirected graph G and an integer k ≥ 0, the NP-hard 2-Layer Planarization problem asks whether G can be transformed into a forest of caterpillar trees by removing at most k edges. Since transforming G into a forest of caterpillar trees requires breaking every cycle, the size f of a minimum feedback edge set is a natural parameter with f ≤ k. We improve on previous fixed-parameter tractability results with respect to k by presenting a problem kernel with O(f) vertices and edges and a new search-tree based algorithm, both with about the same worst-case bounds for f as the previous results for k, although we expect f to be smaller than k for a wide range of input instances.

Supported by the DFG, research projects PABI (NI 369/7) and DARE (GU 1023/1, NI 369/11).

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Authors and Affiliations

  1. Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743, Jena, Germany

    Johannes Uhlmann & Mathias Weller

Authors
  1. Johannes Uhlmann
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  2. Mathias Weller
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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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Uhlmann, J., Weller, M. (2010). Two-Layer Planarization Parameterized by Feedback Edge Set. 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_39

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  • DOI: https://doi.org/10.1007/978-3-642-13562-0_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13561-3

  • Online ISBN: 978-3-642-13562-0

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