Faster Algorithms for δ,γ-Matching and Related Problems

  • Peter Clifford
  • Raphaël Clifford
  • Costas Iliopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3537)


We present new faster algorithms for the problems of δ and (δ, γ)-matching on numeric strings. In both cases the running time of the proposed algorithms is shown to be O(δn log m), where m is the pattern length, n is the text length and δ a given integer. Our approach makes use of Fourier transform methods and the running times are independent of the alphabet size. \(O(n\sqrt{m\log{m}})\) algorithms for the γ-matching and total-difference problems are also given. In all the above cases, we improve existing running time bounds in the literature.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Peter Clifford
    • 1
  • Raphaël Clifford
    • 2
  • Costas Iliopoulos
    • 2
  1. 1.Department of StatisticsOxfordUK
  2. 2.Algorithm Design Group, Department of Computer ScienceKing’s College LondonLondonUK

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