Hyperconvexity and Tight Span Theory for Diversities

Abstract

The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has applications to metric classification and data visualisation. Here we introduce a generalisation of metrics, called diversities, and demonstrate that the rich theory associated to metric tight spans and hyperconvexity extends to a seemingly richer theory of diversity tight spans and hyperconvexity.

revised in response to referee comments

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Cited by in corpus (9)

• Diversities and Conformities
• Trees, Tight-Spans and Point Configuration
• Vertex Decomposition of Steiner Wiener Index and Steiner Betweenness Centrality
• Parsimonious Labeling
• Open Problem Statement: Minimal Distortion Embeddings of Diversities in ${\ell }_1$
• Negative type diversities, a multi-dimensional analogue of negative type metrics
• Diversities and the Geometry of Hypergraphs
• Lattice Diversities
• Diversities, hyperconvexity and fixed points