2 papers
cs.AI2026
The Density of Cross-Persistence Diagrams and Its Applications
Alexander Mironenko, Evgeny. Burnaev, Serguei Barannikov
Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diag…
cs.CG2025
Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization
Ilya Trofimov, Daria Voronkova, Alexander Mironenko +4
We introduce a topological feedback mechanism for the Travelling Salesman Problem (TSP) by analyzing the divergence between a tour and the minimum spanning tree (MST). Our key cont…