The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
Lower bounds for off-line range searching
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
Optimal Biweighted Binary Trees and the Complexity of Maintaining Partial Sums
SIAM Journal on Computing
A Lower Bound on the Complexity of Orthogonal Range Queries
Journal of the ACM (JACM)
The Complexity of Maintaining an Array and Computing Its Partial Sums
Journal of the ACM (JACM)
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
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
Randomization does not help searching predecessors
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
Data Structures for Range Median Queries
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Cell probe lower bounds and approximations for range mode
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Theoretical Computer Science
Space efficient data structures for dynamic orthogonal range counting
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Persistency in suffix trees with applications to string interval problems
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
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
Path queries in weighted trees
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Dynamic range selection in linear space
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Space-efficient data-analysis queries on grids
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The cell probe complexity of dynamic range counting
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Improved range searching lower bounds
Proceedings of the twenty-eighth annual symposium on Computational geometry
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Orthogonal range searching in linear and almost-linear space
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Succinct data structures for path queries
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Mihai Pǎtraşcu: obituary and open problems
ACM SIGACT News
Space-efficient data-analysis queries on grids
Theoretical Computer Science
Compressed persistent index for efficient rank/select queries
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Spaces, Trees, and Colors: The algorithmic landscape of document retrieval on sequences
ACM Computing Surveys (CSUR)
Space efficient data structures for dynamic orthogonal range counting
Computational Geometry: Theory and Applications
Efficient range searching for categorical and plain data
ACM Transactions on Database Systems (TODS)
Compact binary relation representations with rich functionality
Information and Computation
Journal of Discrete Algorithms
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Proving lower bounds for range queries has been an active topic of research since the late 70s, but so far nearly all results have been limited to the (rather restrictive) semigroup model. We consider one of the most basic range problem, orthogonal range counting in two dimensions, and show almost optimal bounds in the group model and the (holy grail) cell-probe model. Specifically, we show the following bounds, which were known in the semigroup model, but are major improvements in the more general models:* In the group and cell-probe models, a static data structure of size n lgO(1) n requires Omega(lg n lglg n) time per query. This is an exponential improvement over previous bounds, and matches known upper bounds.* In the group model, a dynamic data structure takes time Omega((lg n lglg n)2) per operation. This is close to the O(lg2 n) upper bound, where as the previous lower bound was Omega(lg n). Proving such (static and dynamic) bounds in the group model has been regarded as an important challenge at least since [Fredman, JACM 1982] and [Chazelle, FOCS 1986].