A Sublinear Time Randomized Algorithm for Coset Enumeration in the Black Box Model

  • Bin Fu
  • Zhixiang Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


Coset enumeration is for enumerating the cosets of a subgroup H of a finite index in a group G. We study coset enumeration algorithms by using two random sources to generate random elements in a finite group G and its subgroup H. For a finite set S and a real number c > 0, a random generator R S is a c-random source for S if c· min {Pr[a = R S ())|a ∈ S]} ≥ max {Pr[a = R S ())|a ∈ S]}. Let c be an arbitrary constant. We present an \(O({|G|\over \sqrt{|H|}}(\log |G|)^3)\)-time randomized algorithm that, given two respective c-random sources R G for a finite group G and R H for a subgroup H ⊆ G, computes the index \(t={|G|\over |H|}\) and a list of elements a 1,a 2, ⋯ , a t  ∈ G such that a i H ∩ a j H = ∅ for all \(i\not=j\), and \(\cup_{i=1}^t a_iH=G\). This algorithm is sublinear time when |H| = Ω((log|G|)6 + ε ) for some constant ε> 0.


Finite Group Random Element Intersection Graph Algorithm Approximate Great Common Divisor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Bin Fu
    • 1
  • Zhixiang Chen
    • 1
  1. 1.Dept. of Computer ScienceUniversity of TexasPan AmericanUSA

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