Abstract:The Explorer-Director game, first introduced by Nedev and Muthukrishnan, can be described as a game where two players-Explorer and Director-determine the movement of a token on the vertices of a graph. At each time step, the Explorer specifies a distance that the token must move hoping to maximize the amount of vertices ultimately visited, and the Director adversarially chooses where to move token in an effort to minimize this number. Given a graph and a starting vertex, the number of vertices that are visited… Show more
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