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• W2160108357 abstract "Suppose that every k points in a metric space X are D-distortion embeddable into lscr 1. We give upper and lower bounds on the distortion required to embed the entire space X into lscr 1. This is a natural mathematical question and is also motivated by the study of relaxations obtained by lift-and-project methods for graph partitioning problems. In this setting, we show that X can be embedded into lscr 1 with distortion O(D times log(|X|/k)). Moreover, we give a lower bound showing that this result is tight if D is bounded away from I. For D = 1 + delta we give a lower bound of Omega(log(|X|/k/ log( 1/delta)); and for D = 1, we give a lower bound of Omega( log |X|/(log k +log log | X|)). Our bounds significantly improve on the results of Arora, Jjovdsz, Newman, Rabani, Rabinovich and Vempala, who initiated a study of these questions." @default.
• W2160108357 created "2016-06-24" @default.
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• W2160108357 date "2007-10-01" @default.
• W2160108357 modified "2023-09-26" @default.
• W2160108357 title "Hardness of Reconstructing Multivariate Polynomials over Finite Fields" @default.
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• W2160108357 doi "https://doi.org/10.1109/focs.2007.37" @default.
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