Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Optimal parallel pattern matching in strings
Information and Control
Optimal parallel algorithms for string matching
Information and Control
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Lossy on-line dynamic data compression
Sequences
Deterministic sampling: a new technique for fast pattern matching
SIAM Journal on Computing
Efficient pattern matching with scaling
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
A fast string searching algorithm
Communications of the ACM
Efficient string matching: an aid to bibliographic search
Communications of the ACM
Efficient randomized pattern-matching algorithms
IBM Journal of Research and Development - Mathematics and computing
On the Complexity of Finite Sequences
IEEE Transactions on Information Theory
Alphabet independent two dimensional matching
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Highly efficient dictionary matching in parallel
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Optimal parallel two dimensional pattern matching
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
A functional equation often arising in the analysis of algorithms (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Work-time-optimal parallel algorithms for string problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A text compression scheme that allows fast searching directly in the compressed file
ACM Transactions on Information Systems (TOIS)
Three-dimensional pattern matching
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Let sleeping files lie: pattern matching in Z-compressed files
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Two and higher dimensional pattern matching in optimal expected time
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
On Fine and Wilf's theorem for bidimensional words
Theoretical Computer Science
Pattern Matching in Text Compressed by Using Antidictionaries
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
Shift-And Approach to Pattern Matching in LZW Compressed Text
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
Collage system: a unifying framework for compressed pattern matching
Theoretical Computer Science - Selected papers in honour of Setsuo Arikawa
Inplace run-length 2d compressed search
Theoretical Computer Science
On a conjecture on bidimensional words
Theoretical Computer Science
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Optimal discovery of repetitions in 2D
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
A multidimensional critical factorization theorem
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
A general compression algorithm that supports fast searching
Information Processing Letters
Theoretical Computer Science
Simple Random Access Compression
Fundamenta Informaticae
Fast Searching in Packed Strings
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Improved approximate string matching and regular expression matching on Ziv-Lempel compressed texts
ACM Transactions on Algorithms (TALG)
Optimal discovery of repetitions in 2D
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Simple compression code supporting random access and fast string matching
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Fast searching in packed strings
Journal of Discrete Algorithms
Simple Random Access Compression
Fundamenta Informaticae
Improved approximate string matching and regular expression matching on Ziv-Lempel compressed texts
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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String matching is rich with a variety of algorithmic tools. In contrast, multidimensional matching has a rather sparse set of techniques. This paper presents a new algorithmic technique for two-dimensional matching, that of periodicity analysis.Periodicity in strings has been used to solve string matching problems. The success of these algorithms suggests that periodicity can be as important a tool in multidimensional matching. However, multidimensional periodicity is not as simple as it is in strings and was not formally studied or used in pattern matching.This paper's main contribution is defining and analysing two-dimensional periodicity in rectangular arrays. In addition, we introduce a new pattern matching paradigm - Compressed Matching. A text array T and a pattern array P are given in compressed forms c(T) and c(P). We seek all appearances of P in T, without decompressing T. By using periodicity analysis, we show that for the two-dimensional run-length compression there is a O(|c(T)|log|P|+|P|), or almost optimal algorithm that can achieve a search time that is sublinear in the size of the text |T|.