• Corpus ID: 5842763

On the Complexity of Nondeterministically Testable Hypergraph Parameters

@article{Karpinski2015OnTC,
  title={On the Complexity of Nondeterministically Testable Hypergraph Parameters},
  author={Marek Karpinski and Roland Mark{\'o}},
  journal={ArXiv},
  year={2015},
  volume={abs/1503.07093}
}
The paper proves the equivalence of the notions of nondeterministic and deterministic parameter testing for uniform dense hypergraphs of arbitrary order. It generalizes the result previously known only for the case of simple graphs. By a similar method we establish also the equivalence between nondeterministic and deterministic hypergraph property testing, answering the open problem in the area. We introduce a new notion of a cut norm for hypergraphs of higher order, and employ regularity… 
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References

SHOWING 1-10 OF 18 REFERENCES
Complexity of Nondeterministic Graph Parameter Testing
TLDR
The sample complexity of nondeterministically testable graph parameters is studied and existing bounds on it are improved by several orders of magnitude.
Non-Deterministic Graph Property Testing
TLDR
This paper studies certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs, and proves that non-deterministically testable properties are also deterministicallyTestable.
A combinatorial characterization of the testable graph properties: it's all about regularity
TLDR
One of the main open problems in the area of property-testing, which was raised in the 1996 paper of Goldreich, Goldwasser and Ron, is resolved by a purely combinatorial characterization of the graph properties that are testable with a constant number of queries.
A measure-theoretic approach to the theory of dense hypergraphs
Limits of CSP Problems and Efficient Parameter Testing
TLDR
A representation theorem is formulated and proved for compact colored $r-uniform directed hypergraph ($r$-graph) limits, and applied to CSP limits, which investigates the sample complexity of testable parameters and discusses the generalized ground state energies.
Hypergraph limits: A regularity approach
  • Yufei Zhao
  • Mathematics
    Random Struct. Algorithms
  • 2015
TLDR
A new proof and construction of hypergraph limits is given, inspired by the original approach of Lovasz and Szegedy, with the key ingredient being a weak Frieze-Kannan type regularity lemma.
Limits of dense graph sequences
Szemerédi’s Lemma for the Analyst
Abstract.Szemerédi’s regularity lemma is a fundamental tool in graph theory: it has many applications to extremal graph theory, graph property testing, combinatorial number theory, etc. The goal of
Random sampling and approximation of MAX-CSP problems
TLDR
A new efficient sampling method for approximating r-dimensional Maximum Constraint Satisfaction Problems, MAX-rCSP, on n variables up to an additive error εnr, which gives for the first time a polynomial in ε—1 bound on the sample size necessary to carry out the above approximation.
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