Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
Succinct indexable dictionaries with applications to encoding k-ary trees and multisets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Lower bounds on the size of selection and rank indexes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Time-space trade-offs for predecessor search
Proceedings of the thirty-eighth 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
Optimal lower bounds for rank and select indexes
Theoretical Computer Science
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
On the Redundancy of Succinct Data Structures
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Cell probe lower bounds for succinct data structures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Bit-probe lower bounds for succinct data structures
Proceedings of the forty-first annual ACM symposium on Theory of computing
The cell probe complexity of succinct data structures
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
On the size of succinct indices
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
ACM Transactions on Algorithms (TALG)
Everywhere-tight information cost tradeoffs for augmented index
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Succinct representations of permutations and functions
Theoretical Computer Science
The Complexity of Distributions
SIAM Journal on Computing
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
New lower and upper bounds for representing sequences
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Mihai Pǎtraşcu: obituary and open problems
ACM SIGACT News
Succinct sampling from discrete distributions
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Dynamic compressed strings with random access
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Journal of Discrete Algorithms
| Hi-index | 0.00 |
The partial sums problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form Rank(k) = Σki=1 A[i]. The problem has been intensely studied, and features as a subroutine in a number of succinct data structures. We show that, if we answer Rank(k) queries by probing t cells of w bits, then the space of the data structure must be at least n + n/wO(t) bits. This redundancy/probe trade-off is essentially optimal: Patrascu [FOCS'08] showed how to achieve n + n/(w/t)Ω(t) bits. We also extend our lower bound to the closely related Select queries, and to the case of sparse arrays.