A Fully Dynamic Algorithm to Test the Upward Planarity of Single-Source Embedded Digraphs

Rextin, Aimal; Healy, Patrick

doi:10.1007/978-3-642-00219-9_24

Cited by 4 publications

(1 citation statement)

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“…Further related results appear in [6,10,11,15,17,19]; in particular, geometric simultaneous embeddings [4,5] are closely related to the setting we consider in this paper. Contributions focused on the information-visualization aspects of dynamic graphs are surveyed in [2]; further, a survey on temporal graph problems appears in [16].…”

Section: Introductionmentioning

confidence: 96%

Graph Stories in Small Area

Borrazzo

Lozzo

Frati

et al. 2019

Lecture Notes in Computer Science

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We study the problem of drawing a dynamic graph, where each vertex appears in the graph at a certain time and remains in the graph for a fixed amount of time, called the window size. This defines a graph story, i.e., a sequence of subgraphs, each induced by the vertices that are in the graph at the same time. The drawing of a graph story is a sequence of drawings of such subgraphs. To support readability, we require that each drawing is straight-line and planar and that each vertex maintains its placement in all the drawings. Ideally, the area of the drawing of each subgraph should be a function of the window size, rather than a function of the size of the entire graph, which could be too large. We show that the graph stories of paths and trees can be drawn on a 2W × 2W and on an (8W + 1) × (8W + 1) grid, respectively, where W is the window size. These results are constructive and yield linear-time algorithms. Further, we show that there exist graph stories of planar graphs whose subgraphs cannot be drawn within an area that is only a function of W .

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