SIAM Journal on Computing
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
SIAM Journal on Discrete Mathematics
Journal of Algorithms
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
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
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
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Approximate period detection and correction
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
On approximating string selection problems with outliers
Theoretical Computer Science
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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. This paper 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 pseudo-locality and study the period recovery problem under pseudo-local metrics. Examples of pseudo-local metrics are the Hamming distance, the swap distance, and the interchange (or Cayley) distance. We show that for pseudo-local 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 pseudo-local Levenshtein edit metric.