Compact pat trees
Journal of Algorithms
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
Proceedings of the 18th Conference on Foundations of Software Technology and Theoretical Computer Science
Succinct static data structures
Succinct static data structures
Lower bounds on the size of selection and rank indexes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
ACM Computing Surveys (CSUR)
Note: A simple storage scheme for strings achieving entropy bounds
Theoretical Computer Science
A simple storage scheme for strings achieving entropy bounds
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster entropy-bounded compressed suffix trees
Theoretical Computer Science
On the size of succinct indices
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Broadword implementation of rank/select queries
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Succinct representation of dynamic trees
Theoretical Computer Science
Theory and practice of monotone minimal perfect hashing
Journal of Experimental Algorithmics (JEA)
Fast, small, simple rank/select on bitmaps
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Journal of Discrete Algorithms
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We develop a new lower bound technique for data structures. We show an optimal $\Omega(n \lg\lg n / \lg n)$ space lower bounds for storing an index that allows to implement rank and select queries on a bit vector B provided that B is stored explicitly. These results improve upon [Miltersen, SODA'05]. We show $\Omega((m/t) \lg t)$ lower bounds for storing rank/select index in the case where B has m 1-bits in it (e.g. low 0-th entropy) and the algorithm is allowed to probe t bits of B. We simplify the select index given in [Raman et al., SODA'02] and show how to implement both rank and select queries with an index of size $(1 + o(1)) (n \lg\lg n / \lg n) + O(n / \lg n)$ (i.e. we give an explicit constant for storage) in the RAM model with word size $\lg n$.