Self-organizing heuristics for implicit data structures
SIAM Journal on Computing
Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
A tradeoff between search and update time for the implicit dictionary problem
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
Algorithms in C++
Implicit Data Structures for the Dictionary Problem
Journal of the ACM (JACM)
Managing gigabytes (2nd ed.): compressing and indexing documents and images
Managing gigabytes (2nd ed.): compressing and indexing documents and images
Membership in Constant Time and Almost-Minimum Space
SIAM Journal on Computing
Communications of the ACM
A tradeoff between search and update in dictionaries
Information Processing Letters
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
Implicit dictionaries supporting searches and amortized updates in O(log n log log n) time
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Implicit B-Trees: New Results for the Dictionary Problem
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Sparse Table Implementation of Priority Queues
Proceedings of the 8th Colloquium on Automata, Languages and Programming
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Optimal cache-oblivious implicit dictionaries
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Implicit dictionaries with O(1) modifications per update and fast search
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
Optimal in-place algorithms for 3-D convex hulls and 2-D segment intersection
Proceedings of the twenty-fifth annual symposium on Computational geometry
Optimal in-place and cache-oblivious algorithms for 3-d convex hulls and 2-d segment intersection
Computational Geometry: Theory and Applications
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An implicit data structure for the dictionary problem maintains n delta values in the first n locations of an array in such a way that it efficiently supports the operations insert, delete and search. No information other than that in O(1) memory cells and in the input data is to be retained; and the only operations performed on the data values (other than reads and writes) are comparisons. This paper describes the implicit B-tree, a new data structure supporting these operations in O(logBn) block transfers like in regular B-trees, under the realistic assumption that a block stores B = Ω(log n) keys, so that reporting r consecutive keys in sorted order has a cost of O(logB n + r/B) block transfers. En route a number of space efficient techniques for handling segments of a large array in a memory hierarchy are developed. Being implicit, the proposed data structure occupies exactly |n/B| blocks of memory after each update, where n is the number of keys after each update and B is the number of keys contained in a memory block. In main memory, the time complexity of the operations is O(log2 n/log log n), disproving a conjecture of the mid 1980s.