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In the anycasting problem, a sensor wants to report event information to one of sinks or actors. We describe the first localized anycasting algorithms that guarantee delivery for connected multi-sink sensor-actor networks. Let S(x) be the closest actor/sink to sensor x, and |xS(x)| be distance between them. In greedy phase, a node s forwards the packet to its neighbor v that minimizes the ratio of cost cost(|sv|) of sending packet to v (here we specifically apply hop-count and power consumption metrics) over the reduction in distance (|sS(s)|-|vS(v)|) to the closest actor/sink. A variant is to forward to the first neighbor on the shortest weighted path toward v. If none of neighbors reduces that distance then recovery mode is invoked. It is done by face traversal toward the nearest connected actor/sink, where edges are replaced by paths optimizing given cost. A hop count based and two variants of localized power aware anycasting algorithms are described. We prove guaranteed delivery property analytically and experimentally.