Technology Category
Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsSearch and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
Hypergraphs as Metro Maps: Drawing Paths with Few Bends in Trees, Cacti, and Plane 4-Graphs
🤖 AI Summary
This work addresses path-based hypergraph visualization, modeling hyperedges as paths supported on underlying structures—including trees, cacti, and planar graphs with maximum degree four—and simultaneously optimizes three bend metrics: (i) minimizing total bends, (ii) minimizing the maximum bends per path, and (iii) maximizing, by layer, the number of zero-bend, one-bend, etc., paths. We introduce the first systematic multi-objective bend-optimization framework, unifying straight-line drawings (for trees and cacti) and orthogonal drawings (for planar 4-regular graphs), and integrate combinatorial optimization with geometric constraints. Experiments demonstrate that our method significantly reduces bend complexity across diverse structures, enhancing readability and visual quality of hypergraphs rendered as metro maps. The approach provides both theoretical foundations and practical algorithms for automated layout of path-supported hypergraphs.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Minimizing total bends in path-based support drawings
Reducing maximum bends per path in tree and cactus supports
Maximizing low-bend paths in orthogonal plane 4-graph drawings
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hypergraphs represented as metro maps
Minimizing bends in path-based tree drawings
Orthogonal drawings for plane supports degree 4
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2020-12-15Citations: 1
