SIAM Journal on Computing
Fast parallel and serial approximate string matching
Journal of Algorithms
Optimal parallel two dimensional pattern matching
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Alphabet-Independent Two-Dimensional Witness Computation
SIAM Journal on Computing
Sorting permutations by block-interchanges
Information Processing Letters
Two-Dimensional Periodicity in Rectangular Arrays
SIAM Journal on Computing
Optimal parallel two dimension text searching on a CREW PRAM4
Information and Computation
SIAM Journal on Discrete Mathematics
Journal of Algorithms
Introduction to algorithms
Mining Partially Periodic Event Patterns with Unknown Periods
Proceedings of the 17th International Conference on Data Engineering
Solving the String Statistics Problem in Time O(n log n)
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
A Unifying Look at d-Dimensional Periodicities and Space Coverings
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Information and Computation
Optimal parallel algorithms for string matching
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Pattern matching with address errors: rearrangement distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Periodicity and repetitions in parameterized strings
Discrete Applied Mathematics
Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
On the cost of interchange rearrangement in strings
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Fast distance multiplication of unit-Monge matrices
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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Assume that a natural cyclic phenomenon has been measured, but the data is corrupted by errors. The type of corruption is application-dependent and may be caused by measurements errors, or natural features of the phenomenon. We assume that an appropriate metric exists, which measures the amount of corruption experienced. This article studies the problem of recovering the correct cycle from data corrupted by various error models, formally defined as the period recovery problem. Specifically, we define a metric property which we call pseudolocality and study the period recovery problem under pseudolocal metrics. Examples of pseudolocal metrics are the Hamming distance, the swap distance, and the interchange (or Cayley) distance. We show that for pseudolocal metrics, periodicity is a powerful property allowing detecting the original cycle and correcting the data, under suitable conditions. Some surprising features of our algorithm are that we can efficiently identify the period in the corrupted data, up to a number of possibilities logarithmic in the length of the data string, even for metrics whose calculation is NP-hard. For the Hamming metric, we can reconstruct the corrupted data in near-linear time even for unbounded alphabets. This result is achieved using the property of separation in the self-convolution vector and Reed-Solomon codes. Finally, we employ our techniques beyond the scope of pseudo-local metrics and give a recovery algorithm for the non-pseudolocal Levenshtein edit metric.