The Complexity of Some Topological Inference Problems

We give some lower bounds on the description, sample, and computational complexities of the problems of computing dimension, homology, and topological type of a manifold, and detecting singularities for a polyhedron.

Saved in:
Bibliographic Details
Published inFoundations of computational mathematics Vol. 14; no. 6; pp. 1277 - 1285
Main Author Weinberger, Shmuel
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.12.2014
Springer
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Complexity
Computation
Computer Science
Computers
Economics
Foundations
Linear and Multilinear Algebras
Lower bounds
Manifolds
Math Applications in Computer Science
Mathematical problems
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Polyhedrons
Singularities
Topological manifolds
Topological spaces
Topology
United States
Concentration of measure
03D40
60-07
Homeomorphism
Gromov–Hausdorff space
Inference
Entropy
Sample complexity
62G99
51K99
Online AccessGet full text
ISSN1615-3375
1615-3383
DOI10.1007/s10208-013-9152-1

Cover

More Information
Summary:We give some lower bounds on the description, sample, and computational complexities of the problems of computing dimension, homology, and topological type of a manifold, and detecting singularities for a polyhedron.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-013-9152-1