Witnessing and guiding sets of tangles

2025/07/06 by Seibt, Annegret
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.04394

Abstract

Tangles o er a way to indirectly but precisely capture cluster-like though possibly fuzzy substructures in discrete data. In this paper, we analyze witnessing and guiding sets of tangles that can help to find proper cluster candidates for given tangles. We show that every k-tangle has a witnessing set whose size is bounded in an exponential function in k which improves a result of Grohe and Schweizer. Further, we generalize a result of Diestel, Elbracht and Jacobs by providing a characterization of tangles that have a guiding function of some given reliability.

Citations

• Point sets and functions inducing tangles of set separations
• Clustering with Tangles: Algorithmic Framework and Theoretical Guarantees
• Isomorphism Testing for Graphs of Bounded Rank Width
• Profiles of separations: in graphs, matroids and beyond

Related

• Tangles: a structural approach to artificial intelligence in the empirical sciences (Part I)
• Clustering with Tangles: Algorithmic Framework and Theoretical Guarantees
• Tangles and Hierarchical Clustering
• Point sets and functions inducing tangles of set separations
• Computing with Tangles