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Short Plane Supports for Spatial Hypergraphs

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

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 visualizations. In this paper we consider visualizing spatial hypergraphs, where each vertex has a fixed location in the plane. This is the case, e.g., when modeling set systems of geospatial locations as hypergraphs. By applying 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. We first show, from a theoretical point of view, that the problem is NP-hard already under rather mild conditions as well as a negative approximability results. 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. Further, we evaluate the performance and trade-offs between solution quality and speed of several heuristics relative to each other and compared to optimal solutions.

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Notes

Acknowledgments

This work started at Dagstuhl seminar 17332 “Scalable Set Visualizations”. The authors would like to thank Nathalie Henry Riche for providing the data for Fig. 2. TC was supported by the Netherlands Organisation for Scientific Research (NWO, 314.99.117). MvG received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under ERC grant agreement n\(^{\text {o}}\) 319209 (project NEXUS 1492) and the German Research Foundation (DFG) within project B02 of SFB/Transregio 161. WM was partially supported by the Netherlands eScience Centre (NLeSC, 027.015.G02).

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.TU EindhovenEindhovenThe Netherlands
  2. 2.Universität KonstanzKonstanzGermany
  3. 3.TU WienViennaAustria
  4. 4.Peking UniversityBeijingChina

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