Bipath Persistence Modules via Zigzag Covering in Topological Data Analysis
A technique for analyzing bipath persistence modules — persistence over a poset formed from two chains sharing a common top and bottom — by covering that poset with an infinite periodic zigzag. The induced restriction functor sends a bipath module to a zigzag module whose barcode mutually determines the original, so decomposition algorithms, interleaving and bottleneck distances, and algebraic stability all transfer from zigzag to bipath persistence.
2501.00322
This paper studies bipath persistence, one of only three finite-poset settings (alongside single-parameter and zigzag persistence) in which persistence modules always decompose into interval modules.…