Labeled Interleaving Distance for Reeb Graphs
Fangfei Lan, Salman Parsa, Bei Wang

TL;DR
This paper introduces a labeled interleaving distance for Reeb graphs, proving its relation to the ordinary interleaving distance and providing algorithms for its computation, thereby advancing topological data analysis tools.
Contribution
It extends the labeled interleaving distance concept from merge trees to Reeb graphs, establishes its properties, and offers efficient algorithms for contour trees.
Findings
Labeled interleaving distance equals the minimum over labelings of the ordinary interleaving distance.
Efficient algorithms are provided for computing the labeled interleaving distance for contour trees.
Counterexamples show the ordinary interleaving distance is not intrinsic on unlabeled Reeb graphs.
Abstract
Merge trees, contour trees, and Reeb graphs are graph-based topological descriptors that capture topological changes of (sub)level sets of scalar fields. Comparing scalar fields using their topological descriptors has many applications in topological data analysis and visualization of scientific data. Recently, Munch and Stefanou introduced a labeled interleaving distance for comparing two labeled merge trees, which enjoys a number of theoretical and algorithmic properties. In particular, the labeled interleaving distance between merge trees can be computed in polynomial time. In this work, we define the labeled interleaving distance for labeled Reeb graphs. We then prove that the (ordinary) interleaving distance between Reeb graphs equals the minimum of the labeled interleaving distance over all labelings. We also provide an efficient algorithm for computing the labeled interleaving…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Geochemistry and Geologic Mapping · Advanced Clustering Algorithms Research
