The Plurality Problem with Three Colors

  • Martin Aigner
  • Gianluca De Marco
  • Manuela Montangero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2996)

Abstract

The plurality problem with three colors is a game between two participants: Paul and Carol. Suppose we are given n balls colored with three colors. At any step of the game, Paul chooses two balls and asks whether they are of the same color, whereupon Carol answers yes or no. The game ends when Paul either produces a ball a of the plurality color (meaning that the number of balls colored like a exceeds those of the other colors), or when Paul states that there is no plurality. How many questions L(n) does Paul have to ask in the worst case? We show that \(3\lfloor n/2 \rfloor - 2 \leq L(n) \leq \lfloor 5n/3 \rfloor - 2\)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aigner, M.: Combinatorial Search. Wiley, Chichester (1988)MATHGoogle Scholar
  2. 2.
    Aigner, M.: Two colors and more (preprint)Google Scholar
  3. 3.
    Alonso, L., Reingold, E.M., Schott, R.: Determining the majority. Information Processing Letters 47, 253–255 (1993)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Alonso, L., Reingold, E.M., Schott, R.: The average-case complexity of determining the majority. SIAM Journal on Computing 26, 1–14 (1997)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Alonso, L., Chassaing, P., Reingold, E.M., Schott, R.: The chip problem (preprint), Available at http://emr.cs.uiuc.edu/~reingold/chips.ps
  6. 6.
    De Marco, G., Pelc, A.: Randomized algorithms for determining the majority on graphs. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 368–377. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Fisher, M., Salzberg, S.: Finding a majority among n votes. Journal of Algorithms 3, 375–379 (1982)Google Scholar
  8. 8.
    Saks, M.E., Werman, M.: On computing majority by comparisons. Combinatorica 11, 383–387 (1991)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Wiener, G.: Search for a majority element. Journal of Statistical Planning and Inference (to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Martin Aigner
    • 1
  • Gianluca De Marco
    • 2
  • Manuela Montangero
    • 2
  1. 1.Institut für Mathematik IIFreie Universität BerlinBerlinGermany
  2. 2.Istituto di Informatica e TelematicaConsiglio Nazionale delle RicerchePisaItaly

Personalised recommendations