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
Two-Dimensional Periodicity in Rectangular Arrays
SIAM Journal on Computing
Optimal parallel two dimension text searching on a CREW PRAM4
Information and Computation
Mining Partially Periodic Event Patterns with Unknown Periods
Proceedings of the 17th International Conference on Data Engineering
A Unifying Look at d-Dimensional Periodicities and Space Coverings
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
Optimal parallel algorithms for string matching
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
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
Approximated Pattern Matching with the L1 , L2 and L∞ Metrics
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Cycle detection and correction
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Finding longest approximate periodic patterns
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Approximate period detection and correction
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
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The problem of finding the period of a vector V is central to many applications. Let V ′ be a periodic vector closest to V under some metric. We seek this V ′, or more precisely we seek the smallest period that generates V ′. In this paper we consider the problem of finding the closest periodic vector in L p spaces. The measures of "closeness" that we consider are the metrics in the different L p spaces. Specifically, we consider the L 1 , L 2 and L ∞ metrics. In particular, for a given n -dimensional vector V , we develop O (n 2) time algorithms (a different algorithm for each metric) that construct the smallest period that defines such a periodic n -dimensional vector V ′. We call that vector the closest periodic vector of V under the appropriate metric. We also show (three) O (n logn ) time constant approximation algorithms for the (appropriate) period of the closest periodic vector.