Journal of Graph Algorithms and Applications
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Special issue on Selected papers from the Twenty-sixth International Symposium on Graph Drawing and Network Visualization, GD 2018
Short Plane Supports for Spatial Hypergraphs
Vol. 23, no. 3, pp. 463-498, 2019. Regular paper.
Abstract A graph $G=(V,E)$ is a support of a hypergraph $H=(V,S)$ if every hyperedge induces a connected subgraph in $G$. Supports are used for certain types of hypergraph drawings, also known as set visualizations. In this paper we consider visualizing spatial hypergraphs, where each vertex has a fixed location in the plane. This scenario appears when, e.g., modeling set systems of geospatial locations as hypergraphs. Following established aesthetic quality criteria, we are interested in finding supports that yield plane straight-line drawings with minimum total edge length on the input point set $V$. From a theoretical point of view, we first show that the problem is NP-hard already under rather mild conditions, and additionally provide a negative approximability result. Therefore, the main focus of the paper lies on practical heuristic algorithms as well as an exact, ILP-based approach for computing short plane supports. We report results from computational experiments that investigate the effect of requiring planarity and acyclicity on the resulting support length. Furthermore, we evaluate the performance and trade-offs between solution quality and speed of heuristics relative to each other and compared to optimal solutions.
Submitted: November 2018.
Reviewed: January 2019.
Revised: June 2019.
Accepted: June 2019.
Final: July 2019.
Published: September 2019.