Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Adding range restriction capability to dynamic data structures
Journal of the ACM (JACM)
A balanced search tree with O(1) worst case update time
Acta Informatica
The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Introduction to algorithms
Bounded ordered dictionaries in O(loglogN) time and O(n) space
Information Processing Letters
The C programming language
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
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
A constant update time finger search tree
Information Processing Letters
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Fusion trees can be implemented with AC0 instructions only
Theoretical Computer Science
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
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Improved fast interger sorting in linear space
Information and Computation
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
Equivalence between Priority Queues and Sorting
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Trans-Dichotomous Algorithms Without Multiplication - Some Upper and Lower Bounds
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Exponential Structures for Efficient Cache-Oblivious Algorithms
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Space efficient dynamic stabbing with fast queries
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Sublogarithmic searching without multiplications
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Static Dictionaries on RAMs: Query Time is Necessary and Sufficient
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Faster deterministic sorting and searching in linear space
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Optimal finger search trees in the pointer machine
Journal of Computer and System Sciences - STOC 2002
Deterministic sorting in O(nlog logn) time and linear space
Journal of Algorithms
Time-space trade-offs for predecessor search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Planar Point Location in Sublogarithmic Time
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Equivalence between priority queues and sorting
Journal of the ACM (JACM)
Data Structures with Local Update Operations
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Worst-Case Optimal Adaptive Prefix Coding
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Data Structures for Approximate Orthogonal Range Counting
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Dynamic 3-Sided Planar Range Queries with Expected Doubly Logarithmic Time
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
An empirical evaluation of extendible arrays
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
A fast algorithm for three-dimensional layers of maxima problem
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
On minimising automata with errors
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Top-k document retrieval in optimal time and linear space
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Dynamic Indexability and the Optimality of B-Trees
Journal of the ACM (JACM)
Cross-Document pattern matching
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Connectivity oracles for planar graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Fast local searches and updates in bounded universes
Computational Geometry: Theory and Applications
Range majority in constant time and linear space
Information and Computation
Mihai Pǎtraşcu: obituary and open problems
ACM SIGACT News
Persistent Predecessor Search and Orthogonal Point Location on the Word RAM
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Simple deterministic algorithms for fully dynamic maximal matching
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
New algorithms for binary jumbled pattern matching
Information Processing Letters
LSEQ: an adaptive structure for sequences in distributed collaborative editing
Proceedings of the 2013 ACM symposium on Document engineering
Discrete Applied Mathematics
Cross-document pattern matching
Journal of Discrete Algorithms
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We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures. This leads to an optimal bound of O(&sqrt;log n/log log n) for searching and updating a dynamic set X of n integer keys in linear space. Searching X for an integer y means finding the maximum key in X which is smaller than or equal to y. This problem is equivalent to the standard text book problem of maintaining an ordered set. The best previous deterministic linear space bound was O(log n/log log n) due to Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space. We also get the following worst-case linear space trade-offs between the number n, the word length W, and the maximal key U W: O(min log log n + log n/logW, log log n ⋅ log log U/log log log U). These trade-offs are, however, not likely to be optimal. Our results are generalized to finger searching and string searching, providing optimal results for both in terms of n.