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View all- Patrascu MMitzenmacher MSchulman L(2010)Towards polynomial lower bounds for dynamic problemsProceedings of the forty-second ACM symposium on Theory of computing10.1145/1806689.1806772(603-610)Online publication date: 5-Jun-2010
Lower bounds for linear degeneracy testing
Pages 554 - 560
Abstract
In the late nineties Erickson proved a remarkable lower bound on the decision tree complexity of one of the central problems of computational geometry: given n numbers, do any r of them add up to 0? His lower bound of Ω(n⌈r/2⌉), for any fixed r, is optimal if the polynomials at the nodes are linear and at most r-variate. We generalize his bound to s-variate polynomials for s>>r. Erickson's bound decays quickly as r grows and never reaches above pseudo-polynomial: we provide an exponential improvement. Our arguments are based on three ideas: (i) a geometrization of Erickson's proof technique; (ii) the use of error-correcting codes; and (iii) a tensor product construction for permutation matrices.
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Published: 13 June 2004
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View all- Patrascu MMitzenmacher MSchulman L(2010)Towards polynomial lower bounds for dynamic problemsProceedings of the forty-second ACM symposium on Theory of computing10.1145/1806689.1806772(603-610)Online publication date: 5-Jun-2010
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