More Like this

1. Intrinsic Interleaving Distance for Merge Trees

   https://doi.org/10.1007/s44007-024-00143-9  

   Gasparovic, Ellen; Munch, Elizabeth; Oudot, Steve; Turner, Katharine; Wang, Bei; Wang, Yusu (December 2024, La Matematica)
2. Bi-directional Log-Structured Merge Tree

   https://doi.org/10.1145/3538712.3538730  

   Zhang, Xin; Mao, Qizhong; Eldawy, Ahmed; Hristidis, Vagelis; Sun, Yihan (July 2022, International Conference on Scientific and Statistical Database Management)
3. Decorated merge trees for persistent topology

   https://doi.org/https://doi.org/10.1007/s41468-022-00089-3  

   Curry, Justin; Hang, Haibin; Needham, Tom; Mio, Washington; Okutan, Osman Berat (March 2022, Journal of applied and computational topology)
4. Sketching Merge Trees for Scientific Visualization

   https://doi.org/10.1109/TopoInVis60193.2023.00013  

   Li, Mingzhe; Palande, Sourabh; Yan, Lin; Wang, Bei (October 2023, 2023 Topological Data Analysis and Visualization (TopoInVis))

   Merge trees are a type of topological descriptors that record the connectivity among the sublevel sets of scalar fields. They are among the most widely used topological tools in visualization. In this paper, we are interested in sketching a set of merge trees using techniques from matrix sketching. That is, given a large set T of merge trees, we would like to find a much smaller set of basis trees S such that each tree in T can be approximately reconstructed from a linear combination of merge trees in S. A set of high-dimensional vectors can be approximated via matrix sketching techniques such as principal component analysis and column subset selection. However, until now, there has not been any work on sketching a set of merge trees. We develop a framework for sketching a set of merge trees that combines matrix sketching with tools from optimal transport. In particular, we vectorize a set of merge trees into high-dimensional vectors while preserving their structures and structural relations. We demonstrate the applications of our framework in sketching merge trees that arise from time-varying scientific simulations. Specifically, our framework obtains a set of basis trees as representatives that capture the “modes” of physical phenomena for downstream analysis and visualization. 

   more » « less
5. Bonsai: High-Performance Adaptive Merge Tree Sorting

   https://doi.org/10.1109/ISCA45697.2020.00033  

   Samardzic, Nikola; Qiao, Weikang; Aggarwal, Vaibhav; Chang, Mau-Chung Frank; Cong, Jason (May 2020, Proceedings of the 47th International Symposium on Computer Architecture (ISCA 2020))