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Visibility Drawings of Plane 3-Trees with Minimum Area

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Abstract

A visibility drawing of a plane graph G is a drawing of G where each vertex is drawn as a horizontal line segment and each edge is drawn as a vertical line segment such that the line segments use only grid points as their endpoints. The area of a visibility drawing is the area of the smallest rectangle on the grid which encloses the drawing. A minimum-area visibility drawing of a plane graph G is a visibility drawing of G where the area is the minimum among all possible visibility drawings of G. The area minimization for grid visibility representation of planar graphs is NP-hard. However, the problem can be solved for a fixed planar embedding of a hierarchically planar graph in quadratic time. In this paper, we give a polynomial-time algorithm to obtain minimum-area visibility drawings of plane 3-trees.

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Authors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh

    Rahnuma Islam Nishat, Debajyoti Mondal & Md. Saidur Rahman

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  1. Rahnuma Islam Nishat
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  2. Debajyoti Mondal
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  3. Md. Saidur Rahman
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Correspondence to Rahnuma Islam Nishat.

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Nishat, R.I., Mondal, D. & Rahman, M.S. Visibility Drawings of Plane 3-Trees with Minimum Area. Math.Comput.Sci. 5, 119–132 (2011). https://doi.org/10.1007/s11786-011-0078-1

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  • DOI: https://doi.org/10.1007/s11786-011-0078-1

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