Greedy Rectilinear Drawings

TL;DR

This paper introduces greedy rectilinear drawings where edges are horizontal or vertical, providing algorithms for testing their existence, characterizing universal cases, and enhancing graph readability and routing.

Contribution

It presents the first characterization and efficient algorithms for recognizing and constructing greedy rectilinear drawings, including universal cases and a polynomial-time testing method.

Findings

Linear-time testing algorithm for planar rectilinear representations

Characterization of universal greedy rectilinear representations

Polynomial-time algorithm for a subset of greedy rectilinear instances

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.