Minimum Tree Supports for Hypergraphs and Low-Concurrency Euler Diagrams

  • Boris Klemz
  • Tamara Mchedlidze
  • Martin Nöllenburg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)


In this paper we present an O(n 2(m + logn))-time algorithm for computing a minimum-weight tree support (if one exists) of a hypergraph H = (V,S) with n vertices and m hyperedges. This improves the previously best known algorithm with running time O(n 4 m 2). A support of H is a graph G on V such that each hyperedge in S induces a connected subgraph in G. If G is a tree, it is called a tree support and it is a minimum tree support if its edge weight is minimum for a given edge weight function. Tree supports of hypergraphs have several applications, from social network analysis and network design problems to the visualization of hypergraphs and Euler diagrams. We show in particular how a minimum-weight tree support can be used to generate an area-proportional Euler diagram that satisfies typical well-formedness conditions and additionally minimizes the number of concurrent curves of the set boundaries in the Euler diagram.


Span Tree Minimum Span Tree Tree Support Network Design Problem Support Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Boris Klemz
    • 1
  • Tamara Mchedlidze
    • 1
  • Martin Nöllenburg
    • 1
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of Technology (KIT)Germany

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