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Parameterized Algorithms for Module Map Problems

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Book cover Combinatorial Optimization (ISCO 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10856))

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Abstract

We introduce and study the NP-hard Module Map problem which has as input a graph G with red and blue edges and asks to transform G by at most k edge modifications into a graph which does not contain a two-colored \(K_3\), that is, a triangle with two blue edges and one red edge, a blue \(P_3\), that is, a path on three vertices with two blue edges, and a two-colored \(P_3\), that is, a path on three vertices with one blue and one red edge, as induced subgraph. We show that Module Map can be solved in \(\mathcal {O}(2^k \cdot n^3)\) time on n-vertex graphs and present a problem kernelization with \(\mathcal {O}(k^2)\) vertices.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Frank Sommer & Christian Komusiewicz

Authors
  1. Frank Sommer
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  2. Christian Komusiewicz
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Correspondence to Frank Sommer or Christian Komusiewicz .

Editor information

Editors and Affiliations

  1. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA

    Jon Lee

  2. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” (IASI), CNR, Rome, Italy

    Giovanni Rinaldi

  3. LAMSADE, Université Paris-Dauphine, Paris, France

    A. Ridha Mahjoub

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Sommer, F., Komusiewicz, C. (2018). Parameterized Algorithms for Module Map Problems. In: Lee, J., Rinaldi, G., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2018. Lecture Notes in Computer Science(), vol 10856. Springer, Cham. https://doi.org/10.1007/978-3-319-96151-4_32

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  • DOI: https://doi.org/10.1007/978-3-319-96151-4_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96150-7

  • Online ISBN: 978-3-319-96151-4

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