The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Suffix arrays: a new method for on-line string searches
SIAM Journal on Computing
An analysis of the Burrows—Wheeler transform
Journal of the ACM (JACM)
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
Introduction to Algorithms
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Compact representations of ordered sets
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Rank/select operations on large alphabets: a tool for text indexing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Squeezing succinct data structures into entropy bounds
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
When indexing equals compression: Experiments with compressing suffix arrays and applications
ACM Transactions on Algorithms (TALG)
ACM Computing Surveys (CSUR)
Note: A simple storage scheme for strings achieving entropy bounds
Theoretical Computer Science
Compressed representations of sequences and full-text indexes
ACM Transactions on Algorithms (TALG)
Compressed indexes for dynamic text collections
ACM Transactions on Algorithms (TALG)
A taxonomy of suffix array construction algorithms
ACM Computing Surveys (CSUR)
Succinct indexes for strings, binary relations and multi-labeled trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic entropy-compressed sequences and full-text indexes
ACM Transactions on Algorithms (TALG)
Adaptive searching in succinctly encoded binary relations and tree-structured documents
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Dynamic rank-select structures with applications to run-length encoded texts
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
A framework for dynamizing succinct data structures
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Range queries over a compact representation of minimum bounding rectangles
ER'10 Proceedings of the 2010 international conference on Advances in conceptual modeling: applications and challenges
Compressed self-indices supporting conjunctive queries on document collections
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Succinct representations of dynamic strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Space-efficient construction of Lempel-Ziv compressed text indexes
Information and Computation
ACM Transactions on Algorithms (TALG)
Counting colours in compressed strings
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Space efficient data structures for dynamic orthogonal range counting
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The wavelet trie: maintaining an indexed sequence of strings in compressed space
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
CRAM: compressed random access memory
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Space-efficient data-analysis queries on grids
Theoretical Computer Science
Space efficient data structures for dynamic orthogonal range counting
Computational Geometry: Theory and Applications
Hi-index | 5.23 |
Operations rank and select over a sequence of symbols have many applications to the design of succinct and compressed data structures managing text collections, structured text, binary relations, trees, graphs, and so on. We are interested in the case where the collections can be updated via insertions and deletions of symbols. Two current solutions stand out as the best in the tradeoff of space versus time (when considering all the operations). One solution, by Makinen and Navarro, achieves compressed space (i.e., nH"0+o(nlog@s) bits) and O(lognlog@s) worst-case time for all the operations, where n is the sequence length, @s is the alphabet size, and H"0 is the zero-order entropy of the sequence. The other solution, by Lee and Park, achieves O(logn(1+log@sloglogn)) amortized time and uncompressed space, i.e. nlog"2@s+O(n)+o(nlog@s) bits. In this paper we show that the best of both worlds can be achieved. We combine the solutions to obtain nH"0+o(nlog@s) bits of space and O(logn(1+log@sloglogn)) worst-case time for all the operations. Apart from the best current solution to the problem, we obtain several byproducts of independent interest applicable to partial sums, text indexes, suffix arrays, the Burrows-Wheeler transform, and others.