Wireless sensor networks have been envisioned to be useful in many government forces and civilian applications like for habitat monitoring and target tracking in air force, battlefield surveillance and so on.The problem of least-latency end-to-end multicast routing over adaptively duty-cycled wireless sensor networks when considered. Such networks exhibit a time-dependent feature, where the link cost and transmission latency from one node to other nodes vary constantly in different discrete time moments. It presents distributed algorithm for finding the time-dependent shortest paths to the sink node for all nodes. It presents distributed shortest path maintenance algorithms with low message complexity and space complexity. It proposes suboptimal implementation by using vector compression mechanism.