Three-dimensional pattern matching
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Inplace 2D matching in compressed images
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On the Complexity of Determining the Period of a String
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Inplace run-length 2d compressed search
Theoretical Computer Science
On a conjecture on bidimensional words
Theoretical Computer Science
Generalizations of suffix arrays to multi-dimensional matrices
Theoretical Computer Science
Generalizations of suffix arrays to multi-dimensional matrices
Theoretical Computer Science
Inplace 2D matching in compressed images
Journal of Algorithms
Parallel two dimensional witness computation
Information and Computation
A multidimensional critical factorization theorem
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
Faster two-dimensional pattern matching with rotations
Theoretical Computer Science
Cycle detection and correction
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Cycle detection and correction
ACM Transactions on Algorithms (TALG)
Approximate period detection and correction
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
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We study two-dimensional periodicity, introduced by Amir and Benson. We characterize periods of a two-dimensional array, namely, the vectors such that two copies of the array, one shifted by the vector over the other, overlap without a mismatch. Using this characterization, we design an alphabet-independent linear-time algorithm for two-dimensional witness computation, i.e., an $O(m^2)$-time algorithm that finds periods of an $m\times m$ array as well as witnesses against nonperiods of the array among the vectors whose length is less than $m/4$. The constant in the $O$ notation does not depend on the alphabet size. Combined with the alphabet-independent text-processing algorithm of Amir, Benson, and Farach [SIAM J. Comput., 23 (1994), pp.~313--323], this leads to the first alphabet-independent linear-time algorithm for two-dimensional pattern matching.