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Anypath routing has been proposed to improve the performance of unreliable wireless networks by exploiting the spatial diversity and broadcast nature of the wireless medium. Previous studies on anypath routing have concentrated on finding an anypath, which optimizes a single quality of service (QoS) parameter. In this paper, we study anypath routing subject to multiple constraints. We first prove that the problem is NP-hard when the number of constraints is larger than one. We then present a polynomial time K--approximation algorithm MAP, where K is the number of constraints. Our algorithm is as simple as Dijkstra's shortest path algorithm. Therefore, it is suitable for implementation in wireless routing protocols.