Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Bounded ordered dictionaries in O(loglogN) time and O(n) space
Information Processing Letters
Dynamic Perfect Hashing: Upper and Lower Bounds
SIAM Journal on Computing
Short encodings of planar graphs and maps
Discrete Applied Mathematics
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
Membership in Constant Time and Almost-Minimum Space
SIAM Journal on Computing
List processing in real time on a serial computer
Communications of the ACM
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
Succinct Representation of Balanced Parentheses and Static Trees
SIAM Journal on Computing
A Fast General Methodology for Information-Theoretically Optimal Encodings of Graphs
SIAM Journal on Computing
Space-efficient finger search on degree-balanced search trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Compact representations of separable graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
Compact representations of ordered sets
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching
SIAM Journal on Computing
Representing Trees of Higher Degree
Algorithmica
Compact Hash Tables Using Bidirectional Linear Probing
IEEE Transactions on Computers
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Succinct dynamic dictionaries and trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
An optimal algorithm for the distinct elements problem
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We consider the problem of maintaining a dynamic dictionary T of keys and associated data for which both the keys and data are bit strings that can vary in length from zero up to the length w of a machine word. We present a data structure for this variable-bit-length dictionary problem that supports constant time lookup and expected amortized constant-time insertion and deletion. It uses O(m + 3n − nlog2n) bits, where n is the number of elements in T, and m is the total number of bits across all strings in T (keys and data). Our dictionary uses an array A[1 … n] in which locations store variable-bit-length strings. We present a data structure for this variable-bit-length array problem that supports worst-case constant-time lookups and updates and uses O(m + n) bits, where m is the total number of bits across all strings stored in A. The motivation for these structures is to support applications for which it is helpful to efficiently store short varying-length bit strings. We present several applications, including representations for semidynamic graphs, order queries on integers sets, cardinal trees with varying cardinality, and simplicial meshes of d dimensions. These results either generalize or simplify previous results.