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We present a fast combinatorial 3/4-approximation algorithm for the maximum asymmetric TSP with weights zero and one. The approximation factor of this algorithm matches the currently best one given by Bläser in 2004 and based on linear programming. Our algorithm first computes a maximum size matching and a maximum weight cycle cover without certain cycles of length two but possibly with half-edges - a half-edge of a given edge e is informally speaking a half of e that contains one of thearXiv:1408.1431v1 fatcat:rs5ogz3azba2tk3afbsjjhnq3y