Abstract
One of the first algorithmic results in graph drawing was how to find a planar straight-line drawing such that vertices are at grid-points with polynomial coordinates. But not until 2007 was it proved that finding such a grid-drawing with optimal area is NP-hard, and the result was only for disconnected graphs.
In this paper, we show that for graphs with bounded treewidth, we can find area-optimal planar straight-line drawings in one of the following two scenarios: (1) when faces have bounded degree and the planar embedding is fixed, or (2) when we want all faces to be drawn convex. We also give NP-hardness results to show that none of these restrictions can be dropped. In particular, finding area-minimal drawings is NP-hard for triangulated graphs minus one edge.
Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research initiated while participating at Dagstuhl seminar 13421. The author would like to thank Martin Vatshelle; many ideas in this paper were strongly inspired by [1].
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Biedl, T. (2014). On Area-Optimal Planar Graph Drawings. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_17
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DOI: https://doi.org/10.1007/978-3-662-43948-7_17
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