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» Randomized Algorithms and Complexity Theory
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STOC
1996
ACM
197views Algorithms» more  STOC 1996»
15 years 7 months ago
Computing Betti Numbers via Combinatorial Laplacians
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...
Joel Friedman
150
Voted
COMPGEOM
2011
ACM
14 years 7 months ago
An output-sensitive algorithm for persistent homology
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...
Chao Chen, Michael Kerber
ECCC
2007
86views more  ECCC 2007»
15 years 3 months ago
On Parameterized Approximability
Abstract. Combining classical approximability questions with parameterized complexity, we introduce a theory of parameterized approximability. The main intention of this theory is ...
Yijia Chen, Martin Grohe, Magdalena Grüber
ALGORITHMICA
1999
99views more  ALGORITHMICA 1999»
15 years 3 months ago
A Note on the Expected Time for Finding Maxima by List Algorithms
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...
Luc Devroye
SMI
2007
IEEE
129views Image Analysis» more  SMI 2007»
15 years 9 months ago
Localized Homology
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...
Afra Zomorodian, Gunnar Carlsson