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Multilevel Planarity

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WALCOM: Algorithms and Computation (WALCOM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11355))

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Abstract

In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let \(G = (V, E)\) be a directed graph and let \(\ell : V \rightarrow \mathcal P(\mathbb Z)\) be a function that assigns a finite set of integers to each vertex. A multilevel-planar drawing of G is a planar drawing of G such that the y-coordinate of each vertex \(v \in V\) is \(y(v) \in \ell (v)\), and each edge is drawn as a strictly y-monotone curve.

We present linear-time algorithms for testing multilevel planarity of embedded graphs with a single source and of oriented cycles. Complementing these algorithmic results, we show that multilevel-planarity testing is NP-complete even in very restricted cases.

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Authors and Affiliations

  1. Department of Computer Science, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Lukas Barth, Guido Brückner, Paul Jungeblut & Marcel Radermacher

Authors
  1. Lukas Barth
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  2. Guido Brückner
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  3. Paul Jungeblut
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  4. Marcel Radermacher
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Corresponding author

Correspondence to Marcel Radermacher .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Guwahati, Guwahati, India

    Gautam K. Das

  2. Indian Institute of Technology Guwahati, Guwahati, India

    Partha S. Mandal

  3. Indian Statistical Institute, Kolkata, India

    Krishnendu Mukhopadhyaya

  4. Gunma University, Kiryu, Japan

    Shin-ichi Nakano

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Barth, L., Brückner, G., Jungeblut, P., Radermacher, M. (2019). Multilevel Planarity. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_18

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  • DOI: https://doi.org/10.1007/978-3-030-10564-8_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10563-1

  • Online ISBN: 978-3-030-10564-8

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