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An O(n)-Round Strategy for the Magnus-Derek Game
International University VNU-HCM, Block 6, Linh Trung Ward, Thu Duc District, HCM City, Vietnam
Received: 8 June 2010; in revised form: 6 July 2010 / Accepted: 8 July 2010 / Published: 15 July 2010
Abstract: We analyze further the Magnus-Derek game, a two-player game played on a round table with n positions. The players jointly control the movement of a token. One player, Magnus, aims to maximize the number of positions visited while minimizing the number of rounds. The other player, Derek, attempts to minimize the number of visited positions. We present a new strategy for Magnus that succeeds in visiting the maximal number of positions in 3(n – 1) rounds, which is the optimal number of rounds up to a constant factor.
Keywords: algorithmic game theory; additive combinatorics; combinatorial games
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Nedev, Z. An O(n)-Round Strategy for the Magnus-Derek Game. Algorithms 2010, 3, 244-254.
Nedev Z. An O(n)-Round Strategy for the Magnus-Derek Game. Algorithms. 2010; 3(3):244-254.
Nedev, Zhivko. 2010. "An O(n)-Round Strategy for the Magnus-Derek Game." Algorithms 3, no. 3: 244-254.