Drawing Algorithms for Linear Diagrams

It is known that drawing linear diagrams with few line segments produces cognitively effective diagrams. However, methods to minimise the number of line segments in a diagram have not been investigated. In this Abstract, we report on four different approaches to drawing linear diagrams: creating a drawing order based on sets; creating a drawing order based on set-intersections; simulated annealing; and a transformation to another problem, in this case the Travelling Salesman Problem (TSP). We tested each of these approaches on a corpus of 440 linear diagrams with a range of characteristics. The algorithm which produced the lowest number of line segments in a diagram was based on the Lin-Kernighan algorithm for solving instances of TSP. The second contribution of the work is the corpus of 440 linear diagrams, which can be used as a benchmark set of problems for others who seek other solutions to the problem of drawing linear diagrams.