Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Bounded ordered dictionaries in O(loglogN) time and O(n) space
Information Processing Letters
Finding level-ancestors in trees
Journal of Computer and System Sciences
Efficient pattern-matching with don't cares
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Algorithms for Finding Level Ancestors in Dynamic Trees
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Efficient Randomized Dictionary Matching Algorithms (Extended Abstract)
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Application of Lempel--Ziv factorization to the approximation of grammar-based compression
Theoretical Computer Science
Faster Suffix Tree Construction with Missing Suffix Links
SIAM Journal on Computing
Efficient randomized pattern-matching algorithms
IBM Journal of Research and Development - Mathematics and computing
The level ancestor problem simplified
Theoretical Computer Science - Latin American theorotical informatics
Real-Time Traversal in Grammar-Based Compressed Files
DCC '05 Proceedings of the Data Compression Conference
Substring compression problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for substring near neighbor problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The string edit distance matching problem with moves
ACM Transactions on Algorithms (TALG)
Exact and Approximate Pattern Matching in the Streaming Model
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Random access to grammar-compressed strings
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A universal algorithm for sequential data compression
IEEE Transactions on Information Theory
Compression of individual sequences via variable-rate coding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Self-Indexed Grammar-Based Compression
Fundamenta Informaticae
Time-Space trade-offs for longest common extensions
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string S of size N compressed by a context-free grammar of size n that answers fingerprint queries. That is, given indices i and j, the answer to a query is the fingerprint of the substring S[i,j]. We present the first O(n) space data structures that answer fingerprint queries without decompressing any characters. For Straight Line Programs (SLP) we get O(logN) query time, and for Linear SLPs (an SLP derivative that captures LZ78 compression and its variations) we get O(loglogN) query time. Hence, our data structures has the same time and space complexity as for random access in SLPs. We utilize the fingerprint data structures to solve the longest common extension problem in query time O(logNlogℓ) and O(logℓloglogℓ+loglogN) for SLPs and Linear SLPs, respectively. Here, ℓ denotes the length of the LCE.