CS231: Topics in Combinatorial Algorithms
Prof. Suri
Homework Assignment 2
Handed Out: Oct. 12
Due: Oct. 21
1. Consider the following game, defined on a bipartite graph
G
= (
X
∪
Y, E
), where
X
is a set of
n
actresses,
Y
is a set of
n
actors, and there there is an edge (
x, y
) if
x
and
y
have costarred in a movie.
The game is played between two players,
P
1
and
P
2
, who take turns. Initially, the
player
P
1
names an actress, say,
x
1
∈
X
. Then, the player
P
2
must name an actor
y
1
who has costarred with
x
1
in some movie. The player
P
1
must now name an
actress
x
2
who has starred with actor
y
1
in a movie, and so on, thereby generating a
sequence
x
1
, y
1
, x
2
, y
2
, . . .
, until one of the players cannot name his actor or actress.
This player (who fails to name the last actor/actress) is the
loser
in this game.
Give a polynomialtime algorithm to decide which of the two players (
P
1
or
P
2
) can
force a win for a given instance of the game.
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 Fall '09
 Vandam
 Graph Theory, Bipartite graph, polynomialtime algorithm, Combinatorial Algorithms

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