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DOI: 10.7155/jgaa.00530
Graph Stories in Small Area
Vol. 24, no. 3, pp. 269292, 2020. Regular paper.
Abstract 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 straightline 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 $2W \times 2W$ and on an $(8W+1) \times (8W+1)$ grid, respectively, where $W$ is the window size. These results are constructive and yield lineartime 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 $W$.

Submitted: October 2019.
Reviewed: February 2020.
Revised: March 2020.
Accepted: April 2020.
Final: April 2020.
Published: May 2020.
Communicated by
Giuseppe Liotta
