Hypergraphs as Metro Maps: Drawing Paths with Few Bends in Trees, Cacti, and Plane 4-Graphs

TL;DR

This paper explores methods for drawing hypergraph supports as metro maps, focusing on minimizing bends in paths within trees, cacti, and plane graphs, using straight-line and orthogonal drawing techniques.

Contribution

It introduces new algorithms for constructing metro map-like drawings of hypergraph supports with optimized bend minimization in various graph classes.

Findings

Efficient algorithms for bend minimization in tree and cactus supports.

Methods for orthogonal drawings of plane supports with degree constraints.

Analysis of bend distribution to maximize 0-bend and 1-bend paths.

Abstract

A hypergraph consists of a set of vertices and a set of subsets of vertices, called hyperedges. In the metro map metaphor, each hyperedge is represented by a path (the metro line) and the union of all these paths is the support graph (metro network) of the hypergraph. Formally speaking, a path-based support is a graph together with a set of paths. We consider the problem of constructing drawings of path-based supports that (i) minimize the sum of the number of bends on all paths, (ii) minimize the maximum number of bends on any path, or (iii) maximize the number of 0-bend paths, then the number of 1-bend paths, etc. We concentrate on straight-line drawings of path-based tree and cactus supports as well as orthogonal drawings of path-based plane supports with maximum degree 4.