# Multi-scale Cycle Tracking in Dynamic Planar Graphs

arXiv: https://arxiv.org/abs/2409.06476 · HTML: https://mlsanity.com/paper/2409.06476/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 49 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 7 of 7)

- [Wasserstein Distances, Geodesics and Barycenters of Merge Trees](https://mlsanity.com/paper/2107.07789/) (2021)
- [Edit Distance between Merge Trees](https://mlsanity.com/paper/2207.08511/) (2022)
- [Inviwo -- A Visualization System with Usage Abstraction Levels](https://mlsanity.com/paper/1811.12517/) (2018)
- [Topology-Based Feature Design and Tracking for Multi-Center Cyclones](https://mlsanity.com/paper/2011.08676/) (2020)
- [Branch Decomposition-Independent Edit Distances for Merge Trees](https://mlsanity.com/paper/2204.02919/) (2022)
- [Merge Tree Geodesics and Barycenters with Path Mappings](https://mlsanity.com/paper/2308.03672/) (2023)
- [Probabilistic Gradient-Based Extrema Tracking](https://mlsanity.com/paper/2308.08956/) (2023)

## Abstract (arXiv)

This paper presents a nested tracking framework for analyzing cycles in 2D force networks within granular materials. These materials are composed of interacting particles, whose interactions are described by a force network. Understanding the cycles within these networks at various scales and their evolution under external loads is crucial, as they significantly contribute to the mechanical and kinematic properties of the system. Our approach involves computing a cycle hierarchy by partitioning the 2D domain into segments bounded by cycles in the force network. We can adapt concepts from nested tracking graphs originally developed for merge trees by leveraging the duality between this partitioning and the cycles. We demonstrate the effectiveness of our method on two force networks derived from experiments with photoelastic disks.