We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a number of advantages over other methods, both in theory and in practice. It requ...
In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homo...
Abstract. Combining classical approximability questions with parameterized complexity, we introduce a theory of parameterized approximability. The main intention of this theory is ...
Maxima in Rd are found incrementally by maintaining a linked list and comparing new elements against the linked list. If the elements are independent and uniformly distributed in t...
In this paper, we introduce localized homology, a theory for finding local geometric descriptions for topological attributes. Given a space and a cover of subspaces, we construct...