Efficient Approximation of the Matching Distance for 2-Parameter Persistence

Explore an efficient algorithm for approximating the matching distance between 2-parameter persistence modules in this 30-minute conference talk. Delve into the computational aspects of topological data analysis, focusing on a tractable measure for comparing multi-filtered simplicial complexes. Learn about the joint work with Michael Kerber that improves upon the quad-tree refinement strategy introduced by Biasotti et al. Discover how local adaptive bounds enable more effective pruning of quad tree regions, leading to enhanced efficiency in approximating the matching distance to any desired precision ε. Gain insights into this important lower bound for the NP-hard interleaving distance problem in multi-parameter persistence.