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On the Characterization of Plane Bus Graphs

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Algorithms and Complexity (CIAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7878))

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Abstract

Bus graphs are being used for the visualization of hyperedges, for example in VLSI design. Formally, they are specified by bipartite graphs G = (B ∪ V,E) of bus vertices B realized by single horizontal and vertical segments, and point vertices V that are connected orthogonally to the bus segments without any bend. The decision whether a bipartite graph admits a bus realization is NP-complete. In this paper we show that in contrast the question whether a plane bipartite graph admits a planar bus realization can be answered in polynomial time.

We first identify three necessary conditions on the partition B = B V  ∪ B H of the bus vertices, here B V denotes the vertical and B H the horizontal buses. We provide a test whether good partition, i.e., a partition obeying these conditions, exist. The test is based on the computation of maximum matching on some auxiliary graph. Given a good partition we can construct a non-crossing realization of the bus graph on an O(n)×O(n) grid in linear time.

Our Research is partially supported by EuroGIGA project GraDR 10-EuroGIGA-OP-003.

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Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany

    Till Bruckdorfer & Michael Kaufmann

  2. Institut für Mathematik, Technische Universität Berlin, Germany

    Stefan Felsner

Authors
  1. Till Bruckdorfer
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  2. Stefan Felsner
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  3. Michael Kaufmann
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Editor information

Editors and Affiliations

  1. School of Engineering, Department of Computer Engineering and Informatics, University of Patras, 265 00, Patras, Greece

    Paul G. Spirakis

  2. LSI Department, Edif Omega, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona 1-3, 08034, Barcelona, Spain

    Maria Serna

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Bruckdorfer, T., Felsner, S., Kaufmann, M. (2013). On the Characterization of Plane Bus Graphs. In: Spirakis, P.G., Serna, M. (eds) Algorithms and Complexity. CIAC 2013. Lecture Notes in Computer Science, vol 7878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38233-8_7

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  • DOI: https://doi.org/10.1007/978-3-642-38233-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38232-1

  • Online ISBN: 978-3-642-38233-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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