Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Lower bounds for union-split-find related problems on random access machines
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Small forwarding tables for fast routing lookups
SIGCOMM '97 Proceedings of the ACM SIGCOMM '97 conference on Applications, technologies, architectures, and protocols for computer communication
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A strong lower bound for approximate nearest neighbor searching
Information Processing Letters
An Optimal Randomised Cell Probe Lower Bound for Approximate Nearest Neighbour Searching
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Time-space trade-offs for predecessor search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Higher Lower Bounds for Near-Neighbor and Further Rich Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Tight lower bounds for selection in randomly ordered streams
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Confluently Persistent Tries for Efficient Version Control
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Cell-probe lower bounds for succinct partial sums
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast prefix search in little space, with applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
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At STOC'06, we presented a new technique for proving cell-probe lower bounds for static data structures with deterministic queries. This was the first technique which could prove a bound higher than communication complexity, and it gave the first separation between data structures with linear and polynomial space. The new technique was, however, heavily tuned for the deterministic worst-case, demonstrating long query times only for an exponentially small fraction of the input. In this paper, we extend the technique to give lower bounds for randomized query algorithms with constant error probability. Our main application is the problem of searching predecessors in a static set of n integers, each contained in a l-bit word. Our trade-off lower bounds are tight for any combination of parameters. For small space, i.e. n1+o(1), proving such lower bounds was inherently impossible through known techniques. An interesting new consequence is that for near linear space, the classic van Emde Boas search time of O(lg l) cannot be improved, even if we allow randomization. This is a separation from polynomial space, since Beame and Fich [STOC'02] give a predecessor search time of O(lg l/lg lg l) using quadratic space. We also show a tight Ω(lg lg n) lower bound for 2-dimensional range queries, via a new reduction. This holds even in rank space, where no superconstant lower bound was known, neither randomized nor worst-case. We also slightly improve the best lower bound for the approximate nearest neighbor problem, when small space is available.