Probabilistic strategies for the partition and plurality problems

  • Authors:

  • Zdeněk Dvořák;Vít Jelínek;Daniel Král';Jan Kynčl;Michael Saks

  • Affiliations:

  • Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00 Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00 Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00 Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00 Prague, Czech Republic;Department of Mathematics, Rutgers, State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019

  • Venue:
  • Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
  • Year:
  • 2007

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Abstract

We consider a game played by two players, Paul and Carol. Carolfixes a coloring of n balls with three colors. At each step,Paul chooses a pair of balls and asks Carol whether the balls havethe same color. Carol truthfully answers yes or no. In thePlurality problem, Paul wants to find a ball with the most commoncolor. In the Partition problem, Paul wants to partition the ballsaccording to their colors. Paul's goal is to ask Carol the fewestnumber of questions to reach his goal. We find optimalprobabilistic strategies for the Partition problem and thePlurality problem in the considered setting. © 2006 WileyPeriodicals, Inc. Random Struct. Alg., 2007