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Detecting Approximate Periodic Patterns

  • Amihood Amir
  • Alberto Apostolico
  • Estrella Eisenberg
  • Gad M. Landau
  • Avivit Levy
  • Noa Lewenstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7659)

Abstract

Given ε ∈ [0, 1), the ε-Relative Error Periodic Pattern Problem (REPP) is the following:

INPUT: An n-long sequence S of numbers s i  ∈ ℕ in increasing order.

OUTPUT: The longest ε-relative error periodic pattern, i.e., the longest subsequence \(s_{i_1}, s_{i_2},\ldots, s_{i_k}\) of S, for which there exists a number p such that the absolute difference between any two consecutive numbers in the subsequence is at least p and at most p(1 + ε).

The best known algorithm for this problem has O(n 3) time complexity. This bound is too high for large inputs in practice. In this paper we give a new algorithm for finding the longest ε-relative error periodic pattern (the REPP problem). Our method is based on a transformation of the input sequence into a different representation: the ε-active maximal intervals list L, defined in this paper. We show that the transformation of S to the list L can be done efficiently (quadratic in n and linear in the size of L) and prove that our algorithm is linear in the size of L. This enables us to prove that our algorithm works in sub-cubic time on inputs for which the best known algorithm works in O(n 3) time. Moreover, though it may happen that our algorithm would still be cubic, it is never worse than the known O(n 3)-algorithm and in many situations its complexity is O(n 2) time.

Keywords

Input Sequence Arithmetic Progression Periodic Pattern Maximal Interval Active Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bagchi, S., Hung, E., Iyengar, A., Vogl, N.G., Wadia, N.: Capacity planning tools for web and grid environments. In: Proc. 1st International Conference on Performance Evaluation Methodolgies and Tools, VALUETOOLS (2006) ISBN = 1-59593-504-5, article number 25, http://doi.acm.org/10.1145/1190095
  2. 2.
    Gfeller, B.: Finding Longest Approximate Periodic Patterns. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 463–474. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Han, J., Dong, G., Yin, Y.: Efficient mining of partial periodic patterns in time series database. In: Proc. of the 15th International Conference on Data Engineering (ICDE 1999), pp. 106–115. IEEE Computer Society (1999)Google Scholar
  4. 4.
    Ma, S., Hellerstein, J.L.: Mining partially periodic event patterns with unknown periods. In: The 17th International Conference on Data Engineering (ICDE), pp. 205–214. IEEE Computer Society (2001)Google Scholar
  5. 5.
    Federal Highway Administration U.S. Department of Transportation, Conjestion: a national issue (August 2011), http://www.ops.fhwa.dot.gov/aboutus/opstory.htm
  6. 6.
    Panteleenko, V.V.: Instantaneous offloading of web server loads, Ph.D. thesis. University of Notre Dame (2002)Google Scholar
  7. 7.
    Rasheed, F., Alshalalfa, M., Alhajj, R.: Efficient periodicity mining in time series databases using suffix trees. IEEE Transactions on Knowledge and Data Engineering 99(preprints) (2010)Google Scholar
  8. 8.
    Tanbeer, S., Ahmed, C., Jeong, B.-S., Lee, Y.-K.: Discovering Periodic-Frequent Patterns in Transactional Databases. In: Theeramunkong, T., Kijsirikul, B., Cercone, N., Ho, T.-B. (eds.) PAKDD 2009. LNCS, vol. 5476, pp. 242–253. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Yang, J., Wang, W., Yu, P.S.: Mining asynchronous periodic patterns in time series data. IEEE Trans. on Knowl. and Data Eng. (15), 613–628 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Amihood Amir
    • 1
    • 2
  • Alberto Apostolico
    • 3
    • 4
  • Estrella Eisenberg
    • 1
  • Gad M. Landau
    • 5
    • 6
  • Avivit Levy
    • 7
    • 8
  • Noa Lewenstein
    • 9
  1. 1.Department of Computer ScienceBar-Ilan UniversityRamat-GanIsrael
  2. 2.Department of Computer ScienceJohns Hopkins UniversityBaltimoreUnited States
  3. 3.College of ComputingGeorgia Institute of TechnologyAtlantaUSA
  4. 4.Dipartimento di Ingegneria dell’ InformazioneUniversità diPadovaPadovaItaly
  5. 5.Department of Computer ScienceUniversity of HaifaHaifaIsrael
  6. 6.Department of Computer Science and EngineeringPolytechnic Institute of New York UniversityBrooklynUnited States
  7. 7.Department of Software EngineeringShenkar CollegeRamat-GanIsrael
  8. 8.CRIHaifa UniversityHaifaIsrael
  9. 9.Netanya CollegeNetanyaIsrael

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