A linear algorithm to find a rectangular dual of a planar triangulated graph

Bhasker, J.; Sahni, Sartaj

doi:10.1007/bf01762117

Cited by 83 publications

(29 citation statements)

References 4 publications

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“…(5) The resulting graph is triangulated with the algorithm described in 9 The graph obtained after these transformations admits a rectangular dual, that can be computed in linear time with several algorithms. 5,10 However, this procedure does not run in linear time and is fairly complicated, as it requires structuring the graph in step 3. Instead, we are investigating an algorithm that works on the plain graph and exploits matching in cubic graphs, that can be computed in linear time, as shown in.…”

Section: Ocord: Optimal Constructor Of a Rectangular Dualmentioning

confidence: 99%

Rectangular Dualization of Biconnected Planar Graphs in Linear Time and Related Applications

Ancona

Drago

Quercini

et al. 2007

Applied and Industrial Mathematics in Italy II

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http://www.it.uts.edu.au Although rectangular dualization has been studied for several years in the context of floorplanning problems, its descriptive power has not been fully exploited for graph representation. The main obstacle is that the computation of a rectangular dual of any planar biconnected graph requires a sequence of non-trivial steps, some of which are still under investigation. In particular, the most tricky issue is the optimal management of separating triangles, for which no existing algorithm runs in linear time. In this paper we present our advances in rectangular dualization and we show two applications that, while very different, explain better than others its role.

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Section: Ocord: Optimal Constructor Of a Rectangular Dualmentioning

confidence: 99%

Rectangular Dualization of Biconnected Planar Graphs in Linear Time and Related Applications

Ancona

Drago

Quercini

et al. 2007

Applied and Industrial Mathematics in Italy II

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“…Second, we investigate the connectivity restrictions on the graphs that may be drawn as flat folding patterns. This type of constraint has proven very fruitful in past questions about the geometric realizations of planar graphs, providing complete characterizations of the graphs of convex polyhedra (Steinitz's theorem) [24], drawings with rectangular faces ("rectangular duals") [5,11,16,18], orthogonal polyhedra [10], and two-dimensional soap bubble clusters [9].…”

Section: Introductionmentioning

confidence: 99%

Realization and Connectivity of the Graphs of Origami Flat Foldings

Eppstein

2018

Lecture Notes in Computer Science

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We investigate the graphs formed from the vertices and creases of an origami pattern that can be folded flat along all of its creases. As we show, this is possible for a tree if and only if the internal vertices of the tree all have even degree greater than two. However, we prove that (for unbounded sheets of paper, with a vertex at infinity representing a shared endpoint of all creased rays) the graph of a folding pattern must be 2-vertex-connected and 4-edge-connected.

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“…On the other hand, the research in constructive approaches is less active. Since module connectivities are used for floorplan construction, the adjacency graph (also known as Grason graph [3]) plays a crucial role in these approaches [6,1,7]. In an adjacency graph, an edge represents the adjacency between modules that share a boundary.…”

Section: Introductionmentioning

confidence: 99%

“…Some of these steps are NP-complete [12]. Even though there exists a linear time algorithm in theory [1], generating a floorplan from an adjacency graph is also not an easy process.…”

Section: Introductionmentioning

confidence: 99%

Interconnect estimation without packing via ACG floorplans

Wang

Zhou

2005

Proceedings of the 2005 Conference on Asia South Pacific Design Automation - ASP-DAC '05

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ACG (Adjacent Constraint Graph) is a general floorplan representation. The refinement of constraint graphs gives not only an efficient representation but also a representation sharing the advantage of adjacency graphs. As most edges in an ACG are between modules that are close to each other, the physical distance of two modules can be measured without packing by the shortest path between them on the ACG. Experimental results verified this relationship and possible approaches for interconnect planning are discussed.

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A linear algorithm to find a rectangular dual of a planar triangulated graph

Cited by 83 publications

References 4 publications

Rectangular Dualization of Biconnected Planar Graphs in Linear Time and Related Applications

Rectangular Dualization of Biconnected Planar Graphs in Linear Time and Related Applications

Realization and Connectivity of the Graphs of Origami Flat Foldings

Interconnect estimation without packing via ACG floorplans

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