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ISVD
2010
IEEE
13 years 9 months ago
Alpha Shape Topology of the Cosmic Web
—We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determin...
Rien van de Weygaert, Erwin Platen, Gert Vegter, B...
JC
2007
130views more  JC 2007»
13 years 10 months ago
On the complexity of deciding connectedness and computing Betti numbers of a complex algebraic variety
We extend the lower bounds on the complexity of computing Betti numbers proved in [6] to complex algebraic varieties. More precisely, we first prove that the problem of deciding ...
Peter Scheiblechner
CORR
2007
Springer
139views Education» more  CORR 2007»
13 years 11 months ago
Algorithmic Semi-algebraic Geometry and Topology -- Recent Progress and Open Problems
Abstract. We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms f...
Saugata Basu
STOC
1996
ACM
197views Algorithms» more  STOC 1996»
14 years 3 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