Uncertainty principles, extractors, and explicit embeddings of l2 into l1

  • Authors:
  • Piotr Indyk

  • Affiliations:
  • MIT, Cambridge, MA

  • Venue:
  • Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
  • Year:
  • 2007

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Abstract

We give an explicit construction of a constant distortion embedding F of l2n into l1m, with m=n1+o(1).As a bonus, our embedding also has good computational properties: for any input x, Fx can be computed in n1+o(1) time.The previously known mappings required Ω(n2) evaluation time.