Lower Bounds for Edit Distance and Product Metrics via Poincaré-Type Inequalities

  title={Lower Bounds for Edit Distance and Product Metrics via Poincar{\'e}-Type Inequalities},
  author={Alexandr Andoni and T. S. Jayram and Mihai Patrascu},
We prove that any sketching protocol for edit distance achieving a constant approximation requires nearly logarithmic (in the strings' length) communication complexity. This is an exponential improvement over the previous, doubly-logarithmic, lower bound of [Andoni-Krauthgamer, FOCS'07]. Our lower bound also applies to the Ulam distance (edit distance over non-repetitive strings). In this special case, it is polynomially related to the recent upper bound of [Andoni-Indyk-Krauthgamer, SODA'09… CONTINUE READING

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