The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Complexity models for incremental computation
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Journal of the ACM (JACM)
The Complexity of Maintaining an Array and Computing Its Partial Sums
Journal of the ACM (JACM)
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On dynamic range reporting in one dimension
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Bit-probe lower bounds for succinct data structures
Proceedings of the forty-first annual ACM symposium on Theory of computing
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
Using hashing to solve the dictionary problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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This work present several advances in the understanding of dynamic data structures in the bit-probe model: *We improve the lower bound record for dynamic language membership problems to @W((lgnlglgn)^2). Surpassing @W(lgn) was listed as the first open problem in a survey by Miltersen. *We prove a bound of @W(lgnlglglgn) for maintaining partial sums in Z/2Z. Previously, the known bounds were @W(lgnlglgn) and O(lgn). *We prove a surprising and tight upper bound of O(lgnlglgn) for the greater-than problem, and several predecessor-type problems. We use this to obtain the same upper bound for dynamic word and prefix problems in group-free monoids. We also obtain new lower bounds for the partial-sums problem in the cell-probe and external-memory models. Our lower bounds are based on a surprising improvement of the classic chronogram technique of Fredman and Saks [Michael L. Fredman, Michael E. Saks, The cell probe complexity of dynamic data structures, in: Proc. 21st ACM Symposium on Theory of Computing STOC, 1989, pp. 345-354], which makes it possible to prove logarithmic lower bounds by this approach. Before the work of M. Pa@?trascu and Demaine [Mihai Pa@?trascu, Erik D. Demaine, Logarithmic lower bounds in the cell-probe model, SIAM Journal on Computing 35 (4) (2006) 932-963. See also SODA'04 and STOC'04], this was the only known technique for dynamic lower bounds, and surpassing @W(lgnlglgn) was a central open problem in cell-probe complexity.