Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
NNS lower bounds via metric expansion for l
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Recent years have seen a significant increase in our understanding of high-dimensional nearest neighbor search (NNS) for distances like the `1 and `2 norms. By contrast, our understanding of the `1 norm is now where it was (exactly) 10 years ago. In FOCS’98, Indyk proved the following unorthodox result: there is a data structure (in fact, a decision tree) of size O(n), for any 1, which achieves approximation O(log log d) for NNS in the d-dimensional `1 metric. In this paper, we provide results that indicate that Indyk’s unconventional bound might in fact be optimal. Specifically, we show a lower bound for the asymmetric communication complexity of NNS under `1, which proves that this space/approximation trade-off is optimal for decision treesand for data structures with constant cell-probe complexity.