On finding the rectangular duals of planar triangular graphs
SIAM Journal on Computing
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Optimal Area Algorithm for Planar Polyline Drawings
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Transversal structures on triangulations, with application to straight-line drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Improved floor-planning of graphs via adjacency-preserving transformations
Journal of Combinatorial Optimization
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We present a linear time algorithm that produces a planar polyline drawing for a plane graph with n vertices in a grid of size bounded by (p + 1) × (n - 2), where p ≤ (⌊2n-5/3⌋). It uses at most p ≤ ⌊2n-5/3⌋ bends, and each edge uses at most one bend. Compared with the area optimal polyline drawing algorithm in [3], our algorithm uses a larger grid size bound in trade for a smaller bound on the total number of bends. Their bend bound is (n-2). Our algorithm is based on a transformation from Schnyder's realizers [6,7] of maximal plane graphs to transversal structures [4,5] for maximal internally 4-connected plane graphs. This transformation reveals important relations between the two combinatorial structures for plane graphs, which is of independent interest.