On the Perspectives Opened by Right Angle Crossing Drawings

Abstract

Abstract. Right Angle Crossing (RAC) drawings are polyline drawings where each crossing forms four right angles. RAC drawings have been introduced because cognitive experiments provided evidence that increasing the number of crossings does not decrease the readability of the drawing if the edges cross at right angles. We investigate to what extent RAC drawings can help in overcoming the limitations of widely adopted planar graph drawing conventions, providing both positive and negative results. First, we prove that there exist acyclic planar digraphs not admitting any straight-line upward RAC drawing and that the corresponding decision problem is NP-hard. Also, we show digraphs whose straightline upward RAC drawings require exponential area. Second, we study if RAC drawings allow us to draw bounded-degree graphs with lower curve complexity than the one required by more constrained drawing conventions. We prove that every graph with vertex-degree at most 6 (at most 3) admits a RAC drawing with curve complexity 2 (resp. 1) and with quadratic area. Third, we consider a natural non-planar generalization of planar embedded graphs. Here we give bounds for curve complexity and area different from the ones known for planar embeddings.

A characterization of complete bipartite RAC graphs

“…Angelini edge [1]. A relaxation of RAC drawings, called large angle crossing drawings (drawings where crossings form angles of at most α, for some fixed constant 0 < α < π 2 ) has been studied by several authors: Di Giacomo et al proved bounds and trade-offs on the area requirement and number of bends of large angle crossing drawings [2], and Dujmović et al showed bounds on the number of edges in straight-line large angle crossing drawings [4].…”

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“…Recently, Angelini et al [6] considered some special cases for drawing RAC graphs, for example, acyclic planar RAC digraphs and upward RAC digraphs. They showed that there exist acyclic planar digraphs not admitting any straight-line upward RAC drawing and that the corresponding decision problem is NP-hard.…”

Vertex angle and crossing angle resolution of leveled tree drawings

“…Two main kinds of drawings have been considered: Drawings with crossing angle resolution π 2 (the largest possible value), called Right Angle Crossing drawings (or RAC drawings) (see, e.g., [2,4,5,8,10,11,13,18]), and drawings whose crossing angle resolution is at least a given α ∈ (0, π 2 ) (see, e.g., [1,7,9,12]). …”