Dynamic Grid Embedding with Few Bends and Changes

In orthogonal graph drawing, edges are represented by sequences of horizontal and vertical straight line segments. For graphs of degree at most four, this can be achieved by embedding the graph in a grid. The number of bends displayed is an important criterion for layout quality. A well-known algorithm of Tamassia efficiently embeds a planar graph with fixed combinatorial embedding and vertex degree at most four in the grid such that the number of bends is minimum [23]. When given a dynamic graph, i.e. a graph that changes over time, one has to take into account not only the static criteria of layout quality, but also the effort users spent to regain familiarity with the layout. Therefore, consecutive layouts should compromize between quality and stability. We here extend Tamassia's layout model to dynamic graphs in a way that allows to specify the relative importance of the number of bends vs. the number of changes between consecutive layouts. We also show that optimal layouts in the dynamic model can be computed efficiently by means that are very similar to the static model, namely by solving a minimum cost flow problem in a suitably defined network.