Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Computational geometry: an introduction
Computational geometry: an introduction
Information Processing Letters
The input/output complexity of sorting and related problems
Communications of the ACM
The spatial complexity of oblivious k-probe Hash functions
SIAM Journal on Computing
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
An algorithm for approximate closest-point queries
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Handbook of discrete and computational geometry
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Optimal bounds for the predecessor problem
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Journal of Algorithms - Special issue on SODA '95 papers
Approximate data structures with applications
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Faster deterministic sorting and priority queues in linear space
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Tight(er) worst-case bounds on dynamic searching and priority queues
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Communications of the ACM
Universal Hashing and k-Wise Independent Random Variables via Integer Arithmetic without Primes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Efficient Regular Data Structures and Algorithms for Location and Proximity Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
On dynamic range reporting in one dimension
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
Dynamic indexability and lower bounds for dynamic one-dimensional range query indexes
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Data Structures for Approximate Orthogonal Range Counting
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Algorithms for memory hierarchies: advanced lectures
Algorithms for memory hierarchies: advanced lectures
Counting inversions, offline orthogonal range counting, and related problems
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
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
I/O-efficient data structures for colored range and prefix reporting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Predecessor queries in constant time?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
De dictionariis dynamicis pauco spatio utentibus
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Dynamic Indexability and the Optimality of B-Trees
Journal of the ACM (JACM)
Persistent Predecessor Search and Orthogonal Point Location on the Word RAM
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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We consider static one dimensional range searching problems. These problems are to build static data structures for an integer set S \subseteq U, where U = \{0,1,\dots,2^w-1\}, which support various queries for integer intervals of U. For the query of reporting all integers in S contained within a query interval, we present an optimal data structure with linear space cost and with query time linear in the number of integers reported. This result holds in the unit cost RAM model with word size w and a standard instruction set. We also present a linear space data structure for approximate range counting. A range counting query for an interval returns the number of integers in S contained within the interval. For any constant &egr;0, our range counting data structure returns in constant time an approximate answer which is within a factor of at most 1+&egr; of the correct answer.