Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
The spatial complexity of oblivious k-probe Hash functions
SIAM Journal on Computing
Journal of the ACM (JACM)
Compact pat trees
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Membership in Constant Time and Almost-Minimum Space
SIAM Journal on Computing
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Space-efficient construction of LZ-index
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Succinct representation of triangulations with a boundary
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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A static dictionary is a data structure for storing a subset S of a finite universe U so that membership queries can be answered efficiently. We explore space efficient structures to also find the rank of an element if found. We first give a representation of a static dictionary that takes n lg m + O(lg lg m) bits of space and supports membership and rank (of an element present in S) queries in constant time, where n = |S| and m = |U|. Using our structure we also give a representation of a m-ary cardinal tree with n nodes using n⌈lg m⌉ + 2n + o(n) bits of space that supports the tree navigational operations in O(1) time, when m is o(2lg n= lg lg n). For arbitrary m, we give a structure that takes the same space and supports all the navigational operations, except finding the child labeled i (for any i), in O(1) time. Finding the child labeled i in this structure takes O(lg lg lg m) time.