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.

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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

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Abstract 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.
AbstractList 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.
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.[PUBLICATION ABSTRACT]
Audience Academic
Author Weinberger, Shmuel
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  givenname: Shmuel
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  fullname: Weinberger, Shmuel
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crossref_primary_10_3389_frai_2021_659037
crossref_primary_10_1007_s41468_019_00044_9
Cites_doi 10.2307/1971277
10.1112/plms/s2-17.1.75
10.1007/s00039-002-1161-1
10.1007/BF02776078
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10.1002/9780470317006
10.1090/conm/453/08802
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10.1007/978-3-642-13580-4_6
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Issue 6
Keywords Concentration of measure
03D40
60-07
Homeomorphism
Gromov–Hausdorff space
Inference
Entropy
Sample complexity
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Snippet We give some lower bounds on the description, sample, and computational complexities of the problems of computing dimension, homology, and topological type of...
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SubjectTerms 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
Title The Complexity of Some Topological Inference Problems
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