conference paper published yes Jakub Leśkiewicz author Bartosz Furmanek author Michał Lipiński author dfffb474-4317-11ee-8f5c-fe3fc95a425e0000-0001-9789-9750 Dmitriy Morozov author HeEd department SoCG: Symposium on Computational Geometry IST-BRIDGE: International postdoctoral program project Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some persistent homological features, without affecting the rest. We present a new approach to simplification based on the concept of forbidden regions and combinatorial dynamics. It allows us to reorder and cancel critical values, whose cancellation is not possible using existing methods because they are not consecutive in the total order. Each such cancellation takes O(c⋅n) time in the worst case, where c is the number of birth-death pairs and n is the size of the input complex. https://research-explorer.ista.ac.at/download/22002/22110/2026_LIPIcSSoCG_Leskiewicz.pdf application/pdfno Schloss Dagstuhl - Leibniz-Zentrum für Informatik2026New Brunswick, NJ, United States eng persistent homologytopological simplificationdepth posets 1868-8969 9783959774185 2603.1641610.4230/LIPIcs.SoCG.2026.72 367 Leśkiewicz, Jakub, et al. “Topological Simplification Guided by Forbidden Regions.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 72:1-72:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.72">10.4230/LIPIcs.SoCG.2026.72</a>. Leśkiewicz, Jakub, Bartosz Furmanek, Michał Lipiński, and Dmitriy Morozov. “Topological Simplification Guided by Forbidden Regions.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.72">https://doi.org/10.4230/LIPIcs.SoCG.2026.72</a>. Leśkiewicz J, Furmanek B, Lipiński M, Morozov D. 2026. Topological simplification guided by forbidden regions. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 72:1-72:17. Leśkiewicz J, Furmanek B, Lipiński M, Morozov D. Topological simplification guided by forbidden regions. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.72">10.4230/LIPIcs.SoCG.2026.72</a> J. Leśkiewicz, B. Furmanek, M. Lipiński, and D. Morozov, “Topological simplification guided by forbidden regions,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367. Leśkiewicz, J., Furmanek, B., Lipiński, M., &#38; Morozov, D. (2026). Topological simplification guided by forbidden regions. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.72">https://doi.org/10.4230/LIPIcs.SoCG.2026.72</a> J. Leśkiewicz, B. Furmanek, M. Lipiński, D. Morozov, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. 220022026-06-14T22:01:43Z2026-06-22T07:45:36Z