Core Concepts
Efficiently compute the generalized rank of persistence modules by unfolding to zigzag modules.
Abstract
The article discusses a method to compute the generalized rank of persistence modules by unfolding them into zigzag modules. It introduces the concept of s-completeness and provides an algorithm, GENRANK, to determine the s-complete decomposition of a module. The algorithm iteratively converts full interval modules in a direct decomposition to s-complete modules until all convertible modules are identified. The process involves checking foldability and adding limit modules to make intervals complete. Theoretical propositions support the algorithm's validity and efficiency.
Stats
P-indexed persistence module M defined over poset P.
Rank computation for 2-parameter persistence modules.
Linear time algorithm for degree-1 homology in graphs.
Efficiency comparison with other algorithms.