Optimal algorithms for extracting spatial regularity in images
Pattern Recognition Letters
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Mining Partially Periodic Event Patterns with Unknown Periods
Proceedings of the 17th International Conference on Data Engineering
Mining Asynchronous Periodic Patterns in Time Series Data
IEEE Transactions on Knowledge and Data Engineering
Efficient Mining of Partial Periodic Patterns in Time Series Database
ICDE '99 Proceedings of the 15th International Conference on Data Engineering
Discovering Periodic-Frequent Patterns in Transactional Databases
PAKDD '09 Proceedings of the 13th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining
Efficient Periodicity Mining in Time Series Databases Using Suffix Trees
IEEE Transactions on Knowledge and Data Engineering
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
Detecting approximate periodic patterns
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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Motivated by the task of finding approximate periodic patterns in real-world data, we consider the following problem: Given a sequence S of n numbers in increasing order, and α ∈ [0, 1], find a longest subsequence Τ = s1, s2,..., sk of numbers si ∈ S, ordered as in S, under the condition that maxi=1,...,k-1{si+1-si}/ mini=1,...,k-1{si+1-si}, called the period ratio of Τ, is at most 1+α. We give an exact algorithm with run time O(n3) for this problem. This bound is too high for large inputs in practice. Therefore, we describe an algorithm which approximates the longest periodic pattern present in the input in the following sense: Given constants α and ε, the algorithm computes a subsequence with period ratio at most (1+α)(1+ε), whose length is greater or equal to the longest subsequence with period ratio at most (1+α). This latter algorithm has a much smaller run time of O(n1+γ), where γ 0 is an arbitrarily small positive constant. As a byproduct which may be of independent interest, we show that an approximate variant of the well-known 3SUM problem can also be solved in O(n1+γ + Tsort(n)) time, for any constant γ 0, where Tsort(n) is the time required to sort n numbers.