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Optimal point-set embedding of wheel graphs and a sub-class of 3-trees

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Abstract

In the point-set embeddability problem, given a planar graph and a point set in the plane, one asks if there exists a straight-line drawing of the graph in the plane such that the nodes of the graph are mapped one-to-one onto the points of the set. By optimal embedding of a graph, we mean an embedding of minimum length or area. The point-set embeddability problem is NP-complete, and so far it has been solved polynomially only for a few classes of planar graphs. In this paper, we present optimal \(O(n\log {n})\)-time algorithms for embedding and \(O(n^2)\)-time algorithms for optimal embedding of wheel graphs and a sub-class of 3-trees.

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Authors and Affiliations

  1. Department of Computer Engineering, Islamic Azad University, North Tehran Branch, Tehran, Iran

    Majid Hosseinzadegan & Alireza Bagheri

  2. Department of Computer Engineering and IT, Amirkabir University of Technology, Tehran, Iran

    Alireza Bagheri

Authors
  1. Majid Hosseinzadegan
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  2. Alireza Bagheri
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Correspondence to Majid Hosseinzadegan.

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Hosseinzadegan, M., Bagheri, A. Optimal point-set embedding of wheel graphs and a sub-class of 3-trees. Japan J. Indust. Appl. Math. 33, 621–628 (2016). https://doi.org/10.1007/s13160-016-0232-x

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  • DOI: https://doi.org/10.1007/s13160-016-0232-x

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