Journal of Algorithms
A general approach to dominance in the plane
Journal of Algorithms
Convex Grid Drwaings of Four-Connected Plane Graphs
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Rectangle-of-influence drawings of four-connected plane graphs: extended abstract
APVis '05 proceedings of the 2005 Asia-Pacific symposium on Information visualisation - Volume 45
Closed rectangle-of-influence drawings for irreducible triangulations
Computational Geometry: Theory and Applications
Polynomial area bounds for MST embeddings of trees
Computational Geometry: Theory and Applications
On the area requirements of Euclidean minimum spanning trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Drawing a tree as a minimum spanning tree approximation
Journal of Computer and System Sciences
Planar open rectangle-of-influence drawings with non-aligned frames
GD'11 Proceedings of the 19th international conference on Graph Drawing
Approximate proximity drawings
GD'11 Proceedings of the 19th international conference on Graph Drawing
Approximate proximity drawings
Computational Geometry: Theory and Applications
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We prove that all planar graphs have an open/closed (ε1,ε2)-rectangle of influence drawing for ε10 and ε20, while there are planar graphs which do not admit an open/closed (ε1,0)-rectangle of influence drawing and planar graphs which do not admit a (0,ε2)-rectangle of influence drawing. We then show that all outerplanar graphs have an open/closed (0,ε2)-rectangle of influence drawing for any ε2≥0. We also prove that if ε22 an open/closed (0, ε2)-rectangle of influence drawing of an outerplanar graph can be computed in polynomial area. For values of ε2 such that ε2≤2, we describe a drawing algorithm that computes (0,ε2)-rectangle of influence drawings of binary trees in area $O(n^{2 + f(\varepsilon _2)})$, where f(ε2) is a logarithmic function that tends to infinity as ε2 tends to zero, and n is the number of vertices of the input tree.