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hw2 - CS231 Topics in Combinatorial Algorithms Prof Suri...

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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 co-starred 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 co-starred 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 polynomial-time 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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