Jan
Kynčl
Artificial Intelligence and Image Processing
Department of Mathematics, Rutgers, the State University of NJ, 110 Frelinghuysen Road, 08854-8019, Piscataway, NJ, USA
Department of Mathematics, Rutgers, the State University of NJ, 110 Frelinghuysen Road, 08854-8019, Piscataway, NJ, USA
coloring
https://doi.org/10.1007/978-3-540-31856-9_17
number
2005
Three Optimal Algorithms for Balls of Three Colors
Carol
pairs
Plurality problem
Paul
optimal algorithm
players
algorithm
game
same color
chapters
color
false
least number
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.
n balls
partition problem
206-217
goal
https://scigraph.springernature.com/explorer/license/
problem
common color
2022-12-01T06:53
2005-01-01
chapter
probabilistic strategy
step
questions
strategies
pair of balls
ball
Jelínek
Vít
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
Zdeněk
Dvořák
pub.1032620341
dimensions_id
Springer Nature - SN SciGraph project
Saks
Michael
Springer Nature
STACS 2005
978-3-540-31856-9
978-3-540-24998-6
Information and Computing Sciences
doi
10.1007/978-3-540-31856-9_17
Durand
Bruno
Daniel
Král’
Volker
Diekert