Greedy Rectilinear Drawings
arXiv:1808.09063
The paper studies graph drawings where edges are axis-aligned (horizontal or vertical) and the drawing is greedy, meaning one can always move closer to a target vertex along a path, and provides characterizations and algorithms to test and construct such drawings for planar graphs.
Abstract
A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. The existence of greedy drawings has been widely studied under different topological and geometric constraints, such as planarity, face convexity, and drawing succinctness. We introduce greedy rectilinear drawings, in which each edge is either a horizontal or a vertical segment. These drawings have several properties that improve human readability and support network routing. We address the problem of testing whether a planar rectilinear representation, i.e., a plane graph with specified vertex angles, admits vertex coordinates that define a greedy drawing. We provide a characterization, a linear-time testing algorithm, and a full generative scheme for universal greedy rectilinear representations, i.e., those for which every drawing is greedy. For general greedy rectilinear representations, we give a combinatorial characterization and, based on it, a polynomial-time testing and drawing algorithm for a meaningful subset of instances.
Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)