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This paper introduces the problem of fault-tolerant topology control for all-to-one and one-to-all communication in static wireless networks with asymmetric wireless links. This problem is important in both theoretical and practical aspects. We investigate two approaches, namely, the minimum-weight-based approach and the augmentation-based approach, to address this problem. Furthermore, we prove that the minimum-weight-based approach has a k-approximation algorithm for all-to-one fault-tolerant topology control, where k is the number of node-disjoint paths. When k = 1, this approach solves the minimum power sink tree problem. To the best of our knowledge, this paper is the first to study the fault-tolerant topology control for all-to-one and one-to-all communication in asymmetric static wireless networks and is also the first to demonstrate that the minimum power sink tree problem has a polynomial time optimal solution.