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- W4301490069 abstract "Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic $k$-uniform hypergraphs of bounded complexity, showing that for each $epsilon>0$ the vertex set can be equitably partitioned into a bounded number of parts (in terms of $epsilon$ and the complexity) so that all but an $epsilon$-fraction of the $k$-tuples of parts are homogeneous. We prove that the number of parts can be taken to be polynomial in $1/epsilon$. Our improved regularity lemma can be applied to geometric problems and to the following general question on property testing: is it possible to decide, with query complexity polynomial in the reciprocal of the approximation parameter, whether a hypergraph has a given hereditary property? We give an affirmative answer for testing typical hereditary properties for semi-algebraic hypergraphs of bounded complexity." @default.
- W4301490069 created "2022-10-05" @default.
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- W4301490069 date "2015-02-05" @default.
- W4301490069 modified "2023-10-06" @default.
- W4301490069 title "A polynomial regularity lemma for semi-algebraic hypergraphs and its applications in geometry and property testing" @default.
- W4301490069 doi "https://doi.org/10.48550/arxiv.1502.01730" @default.
- W4301490069 hasPublicationYear "2015" @default.
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