Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Proving or disproving planar straight-line embeddability onto given rectangles
GD'09 Proceedings of the 17th international conference on Graph Drawing
On the hardness of point-set embeddability
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
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Straight-line grid drawings of bounded size is a classical topic in graph drawing. The Graph Drawing Challenge 2006 dealt with minimizing the area of planar straight-line grid drawings. In this paper, we show that it is NP-complete to decide if a planar graph has a planar straight-line drawing on a grid of given size. Furthermore, we present a new iterative approach to compactify planar straight-line grid drawings. In an experimental study, we evaluate the quality of the compactified drawings with respect to the size of the area as well as to other measures.