Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Randomization does not help searching predecessors
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Indexability, concentration, and VC theory
Proceedings of the Third International Conference on SImilarity Search and APplications
Cell probe lower bounds and approximations for range mode
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Proceedings of the Fourth International Conference on SImilarity Search and APplications
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
Range selection and median: tight cell probe lower bounds and adaptive data structures
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Indexability, concentration, and VC theory
Journal of Discrete Algorithms
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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We convert cell-probe lower bounds for polynomial space into stronger lower bound for near-linear space. Our technique applies to any lower bound proved through the richness method. For example, it applies to partial match, and to near-neighbor problems, either for randomized exact search, or for deterministic approximate search (which are thought to exhibit the curse of dimensionality). These problems are motivated by search in large data bases, so near-linear space is the most relevant regime. Typically, richness has been used to imply \Omega(d/ lg n) lower bounds for polynomial-space data structures, where d is the number of bits of a query. This is the highest lower bound provable through the classic reduction to communication complexity. However, for space n lg^{O(1)} n, we now obtain bounds of \Omega(d/ lg d). This is a significant improvement for natural values of d, such as lg^{O(1)} n. In the most important case of d = \Theta(lg n), we have the first superconstant lower bound. From a complexity-theoretic perspective, our lower bounds are the highest known for any static data-structure problem, significantly improving on previous records.