Floor-planning by graph dualization: 2-concave rectilinear modules
SIAM Journal on Computing
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
SIAM Journal on Computing
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
Simple and efficient floor-planning
Information Processing Letters
On finding most optimal rectangular package plans
DAC '82 Proceedings of the 19th Design Automation Conference
Compact floor-planning via orderly spanning trees
Journal of Algorithms
Planar Polyline Drawings via Graph Transformations
Algorithmica
GD'07 Proceedings of the 15th international conference on Graph drawing
Transversal structures on triangulations, with application to straight-line drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
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Let G=(V,E) and G驴=(V驴,E驴) be two graphs, an adjacency-preserving transformation from G to G驴 is a one-to-many and onto mapping from V to V驴 satisfying the following: (1) Each vertex v驴V in G is mapped to a non-empty subset $\mathcal{A}(v)\subset V'$ in G驴. The subgraph induced by $\mathcal{A}(v)$ is a connected subgraph of G驴; (2) if u驴v驴V, then $\mathcal{A}(u)\cap\mathcal{A}(v)=\emptyset$ ; and (3) two vertices u and v are adjacent to each other in G if and only if subgraphs induced by $\mathcal{A}(u)$ and $\mathcal{A}(v)$ are connected in G驴.In this paper, we study adjacency-preserving transformations from plane triangulations to irreducible triangulations (which are internally triangulated, with four exterior vertices and no separating triangles). As one shall see, our transformations not only preserve adjacency well, but also preserve the endowed realizers of plane triangulations well in the endowed transversal structures of the image irreducible triangulations, which may be desirable in some applications.We then present such an application in floor-planning of plane graphs. The expected grid size of the floor-plan of our linear time algorithm is improved to $(\frac{5n}{8}+O(1))\times (\frac{23n}{24}+O(1))$ , though the worst case grid size bound of the algorithm remains $\lfloor\frac{2n+1}{3}\rfloor\times(n-1)$ , which is the same as the algorithm presented in Liao et al. (J. Algorithms 48:441---451, 2003).