David Bryant ; Paul Tupper - Diversities and the Geometry of Hypergraphs

dmtcs:2080 - Discrete Mathematics & Theoretical Computer Science, April 24, 2014, Vol. 16 no. 2 - https://doi.org/10.46298/dmtcs.2080
Diversities and the Geometry of HypergraphsArticle

Authors: David Bryant 1; Paul Tupper 2

  • 1 Department of Mathematics and Statistics
  • 2 Department of Mathematics [Burnaby]

The embedding of finite metrics in 1 has become a fundamental tool for both combinatorial optimization and large-scale data analysis. One important application is to network flow problems as there is close relation between max-flow min-cut theorems and the minimal distortion embeddings of metrics into 1. Here we show that this theory can be generalized to a larger set of combinatorial optimization problems on both graphs and hypergraphs. This theory is not built on metrics and metric embeddings, but on diversities, a type of multi-way metric introduced recently by the authors. We explore diversity embeddings, 1 diversities, and their application to Steiner Tree Packing and Hypergraph Cut problems.

Volume: Vol. 16 no. 2
Section: PRIMA 2013
Published on: April 24, 2014
Submitted on: December 21, 2013
Keywords: Diversities,Metric embedding,Fractional Steiner Tree Packing,Hypergraphs,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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