Persistent homology of semi-algebraic sets

2022/02/19 by Basu, Saugata, Karisani, Negin
#14F25 #55N31 #68W30 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.09591

Abstract

We give an algorithm with singly exponential complexity for computing the barcodes up to dimension ℓ (for any fixed ℓ ≥ 0) of the filtration of a given semi-algebraic set by the sub-level sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity, and generalizes the corresponding results for computing the Betti numbers up to dimension ℓ of semi-algebraic sets with no filtration present.

Related

• Computing the homology functor on semi-algebraic maps and diagrams
• Efficient Computation of Image Persistence
• Complexity and speed of semi-algebraic multi-persistence
• Computing Betti tables and minimal presentations of zero-dimensional persistent homology
• Interleaved computation for persistent homology