An Integer-Linear Program for Bend-Minimization in Ortho-Radial Drawings

TL;DR

This paper introduces an ILP-based method for creating bend-minimized ortho-radial drawings, significantly reducing bends compared to traditional orthogonal drawings and enabling rapid computation for complex embedded graphs.

Contribution

It presents a novel ILP formulation for bend-free ortho-radial representations and a pruning technique for bend-optimal drawings with fixed embedding and flexible central face.

Findings

Bend reduction of 43.8% on average compared to orthogonal drawings.

Rapid computation of ortho-radial drawings for large embedded graphs.

Effective approach for metro system visualizations.

Abstract

An ortho-radial grid is described by concentric circles and straight-line spokes emanating from the circles' center. An ortho-radial drawing is the analog of an orthogonal drawing on an ortho-radial grid. Such a drawing has an unbounded outer face and a central face that contains the origin. Building on the notion of an ortho-radial representation (Barth et al., SoCG, 2017), we describe an integer-linear program (ILP) for computing bend-free ortho-radial representations with a given embedding and fixed outer and central face. Using the ILP as a building block, we introduce a pruning technique to compute bend-optimal ortho-radial drawings with a given embedding and a fixed outer face, but freely choosable central face. Our experiments show that, in comparison with orthogonal drawings using the same embedding and the same outer face, the use of ortho-radial drawings reduces the number of bends by 43.8% on average. Further, our approach allows us to compute ortho-radial drawings of embedded graphs such as the metro system of Beijing or London within seconds.