Using Reinforcement Learning to Optimize the Global and Local Crossing Number

Abstract

Graph drawing concerns the algorithmic visualization of graphs. A good drawing of a graph is easy to read and facilitates solving tasks on the graph. Several properties have been identified to occur in good drawings of graphs. Such properties include a low number of crossings, large angles between edges, short edges, and depicting symmetries. Many of these properties are explicitly measurable metrics. This lets us model a graph-drawing problem as a game where a single player iteratively moves vertices of a straight-line graph drawing to reduce edge crossings. We investigate whether reinforcement learning can discover effective strategies for playing this game. Our reinforcement-learning agent observes the local geometric and structural context of a vertex and selects a movement direction with the goal of reducing either the global or the local crossing number, that is, either the total number of crossings or the maximum number of crossings per edge. We compare the resulting strategies to existing methods and established crossing-minimization heuristics on standard benchmark graphs. While our approach does not out-compete state-of-the-art methods for minimizing the global crossing number, it is competitive and often superior for minimizing the local crossing number.