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• W2023404461 abstract "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].From a technical perspective, we prove a direct-sum theorem for sketching product metrics that is of independent interest. We show that, for any metric X that requires sketch size which is a sufficiently large constant, sketching the max-product metric ld∞(X) requires Ω(d) bits. The conclusion, in fact, also holds for arbitrary two-way communication. The proof uses a novel technique for information complexity based on Poincare inequalities and suggests an intimate connection between non-embeddability, sketching and communication complexity." @default.
• W2023404461 created "2016-06-24" @default.
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• W2023404461 date "2010-01-17" @default.
• W2023404461 modified "2023-10-18" @default.
• W2023404461 title "Lower bounds for edit distance and product metrics via Poincaré-type inequalities" @default.
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• W2023404461 doi "https://doi.org/10.5555/1873601.1873618" @default.
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