Abstract
We give new lower bounds for randomized NNS data structures in the cell probe model based on robust metric expansion for two metric spaces: l ∞ and Earth Mover Distance (EMD) in high dimensions. In particular, our results imply stronger non-embedability for these metric spaces into l 1. The main components of our approach are a strengthening of the isoperimetric inequality for the distribution on l ∞ introduced by Andoni et al [FOCS’08] and a robust isoperimetric inequality for EMD on quotients of the boolean hypercube.
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Kapralov, M., Panigrahy, R. (2012). NNS Lower Bounds via Metric Expansion for l ∞ and EMD . In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_46
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DOI: https://doi.org/10.1007/978-3-642-31594-7_46
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