Fixed-Parameter Algorithms for Computing RAC Drawings of Graphs

TL;DR

This paper explores the computational complexity of creating right-angle crossing (RAC) graph drawings with limited bends, showing that the problem is fixed-parameter tractable when parameterized by certain graph measures.

Contribution

It introduces the first fixed-parameter algorithms for computing RAC drawings with bounded bends based on feedback edge number and vertex cover number.

Findings

Computing RAC drawings with bounded bends is fixed-parameter tractable.

The algorithms are parameterized by feedback edge number and bend count plus vertex cover number.

This advances understanding of the computational boundaries for RAC drawing problems.

Abstract

In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly $90^\circ$, where the number of bends on such polylines is typically restricted in some way. While structural and topological properties of RAC drawings have been the focus of extensive research, little was known about the boundaries of tractability for computing such drawings. In this paper, we initiate the study of RAC drawings from the viewpoint of parameterized complexity. In particular, we establish that computing a RAC drawing of an input graph $G$ with at most $b$ bends (or determining that none exists) is fixed-parameter tractable parameterized by either the feedback edge number of $G$, or $b$ plus the vertex cover number of $G$.