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2004
ACM

Lower bounds for linear degeneracy testing

14 years 3 months ago
Lower bounds for linear degeneracy testing
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 (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. Categories and Subject Descriptors: F.2.0 [Analysis of Algorithms and Problem Complexity]: General General Terms: Theory Additional Key Words and Phrases: Computational geometry, linear decision trees, lower bounds
Nir Ailon, Bernard Chazelle
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2004
Where STOC
Authors Nir Ailon, Bernard Chazelle
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