Three optimal algorithms for balls of three colors

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, Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic;Department of Mathematics, Rutgers, the State University of NJ, Piscataway, NJ
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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Abstract

We consider a game played by two players, Paul and Carol. Carol fixes a coloring of n balls with three colors. At each step, Paul chooses a pair of balls and asks Carol whether the balls have the same color. Carol truthfully answers yes or no. In the Plurality problem, Paul wants to find a ball with the most common color. In the Partition problem, Paul wants to partition the balls according to their colors. He wants to ask Carol the least number of questions to reach his goal. We find optimal deterministic and probabilistic strategies for the Partition problem and an asymptotically optimal probabilistic strategy for the Plurality problem.