Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
On the cell probe complexity of polynomial evaluation
Theoretical Computer Science
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
A lower bound on the complexity of approximate nearest-neighbor searching on the Hamming cube
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Products and Help Bits in Decision Trees
SIAM Journal on Computing
The Complexity of Some Simple Retrieval Problems
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Membership in Constant Time and Almost-Minimum Space
SIAM Journal on Computing
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The Bit Probe Complexity Measure Revisited
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Tighter lower bounds for nearest neighbor search and related problems in the cell probe model
Journal of Computer and System Sciences - Special issue on STOC 2000
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A linear lower bound on index size for text retrieval
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Random Structures & Algorithms
The cell probe complexity of succinct data structures
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
List decoding from erasures: bounds and code constructions
IEEE Transactions on Information Theory
Vector sets for exhaustive testing of logic circuits
IEEE Transactions on Information Theory
Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs
IEEE Transactions on Information Theory - Part 2
On the Redundancy of Succinct Data Structures
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
On the size of succinct indices
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Optimal trade-offs for succinct string indexes
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
LRM-trees: compressed indices, adaptive sorting, and compressed permutations
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Space-Efficient Preprocessing Schemes for Range Minimum Queries on Static Arrays
SIAM Journal on Computing
Succinct representations of permutations and functions
Theoretical Computer Science
Fast Polynomial Factorization and Modular Composition
SIAM Journal on Computing
LRM-Trees: Compressed indices, adaptive sorting, and compressed permutations
Theoretical Computer Science
Hi-index | 5.23 |
We consider time-space tradeoffs for static data structure problems in the cell probe model with word size 1 (the bit probe model). In this model, the goal is to represent n-bit data with s=n+r bits such that queries (of a certain type) about the data can be answered by reading at most t bits of the representation. Ideally, we would like to keep both s and t small, but there are tradeoffs between the values of s and t that limit the possibilities of keeping both parameters small. In this paper, we consider the case of succinct representations, where s=n+r for some redundancyr@?n. For a Boolean version of the problem of polynomial evaluation with preprocessing of coefficients, we show a lower bound on the redundancy-query time tradeoff of the form (r+1)t=@W(n/logn). In particular, for very small redundancies r, we get an almost optimal lower bound stating that the query algorithm has to inspect almost the entire data structure (up to a logarithmic factor). We show similar lower bounds for problems satisfying a certain combinatorial properties of a coding theoretic flavor, and obtain (r+1)t=@W(n) for certain problems. Previously, no @w(m) lower bounds were known on t in the general model for explicit Boolean problems, even for very small redundancies. By restricting our attention to systematic or index structures @f satisfying @f(x)=x@?@f^*(x) for some map @f^* (where @? denotes concatenation), we show similar lower bounds on the redundancy-query time tradeoff for the natural data structuring problems of Prefix Sum and Substring Search.