Abstract
We introduce a new type of graph drawing called rook-drawing . A rook-drawing of a graph G is obtained by placing the n nodes of G on the intersections of a regular grid, such that each row and column of the grid supports exactly one node. This paper focuses on rook-drawings of planar graphs. We first give a linear algorithm to compute a planar straight-line rook-drawing for outerplanar graphs. We then characterize the maximal planar graphs admitting a planar straight-line rook-drawing, which are unique for a given order. Finally, we give a linear time algorithm to compute a polyline planar rook-drawing for plane graphs with at most n − 3 bent edges.
Highlights
Nowadays, large and dynamic graphs are widely used in the context of Big Data, and their visualization is a classical tool for their analysis
As we proved that some plane graphs do not admit a planar rook-drawing with straight lines, we relax the straight-line constraint and look at planar polyline rook-drawings
We observed that no maximal planar graph but the tower graphs admit a planar straight-line rook-drawing
Summary
Large and dynamic graphs are widely used in the context of Big Data, and their visualization is a classical tool for their analysis. On the other hand, when using hierarchical views, the ability to aggregate or de-aggregate sets of nodes is required [1, 11] When doing such operations, it is important to preserve the mental map of the graph [4], as well as to compute the changes in the representation efficiently, both in order to guarantee a smooth use. Dealing with aggregated data consists in stretching the grid to create enough room for the new appearing nodes (see Fig. 1) These operations clearly preserve orthogonal ordering, which is the first type of mental map defined in [14]. De Fraysseix et al showed that every planar graph admits a straight-line drawing on an (n − 2) × (2n − 4) grid [9] Schnyder improved this result by proving the existence of such a drawing on an (n − 2) × (n − 2)-grid [16]. This drawing can be computed in linear time, each edge is bent at most once and the total number of bends is at most n − 3
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
