  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.
