Improved Bounds for the Randomized Decision Tree Complexity of Recursive Majority

  • Frédéric Magniez
  • Ashwin Nayak
  • Miklos Santha
  • David Xiao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)


We consider the randomized decision tree complexity of the recursive 3-majority function. For evaluating height h formulae, we prove a lower bound for the δ-two-sided-error randomized decision tree complexity of (1 − 2δ)(5/2) h , improving the lower bound of (1 − 2δ)(7/3) h given by Jayram, Kumar, and Sivakumar (STOC ’03). Second, we improve the upper bound by giving a new zero-error randomized decision tree algorithm that has complexity at most (1.007) ·2.64946 h . The previous best known algorithm achieved complexity (1.004) ·2.65622 h . The new lower bound follows from a better analysis of the base case of the recursion of Jayram et al. The new algorithm uses a novel “interleaving” of two recursive algorithms.


Decision Tree Boolean Function Recursive Algorithm Hard Distribution Decision Tree Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Frédéric Magniez
    • 1
  • Ashwin Nayak
    • 2
  • Miklos Santha
    • 1
    • 3
  • David Xiao
    • 1
    • 4
  1. 1.LIAFA, Univ. Paris 7, CNRSParisFrance
  2. 2.C&O and IQCU. Waterloo; and Perimeter InstituteWaterlooCanada
  3. 3.Centre for Quantum TechnologiesNational U. of SingaporeSingapore
  4. 4.Univ. Paris-SudOrsayFrance

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