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Latency of information propagating in wireless network is gaining more and more attention recently. This paper studies the problem of t-Latency Bounded Information Propagation (t-LBIP) problem in wireless networks which are represented by unit-disk graphs. So far, no guaranteed approximation algorithm has been achieved for t-LBIP when t驴2. In this paper, we propose a Polynomial Time Approximation Scheme for t-LBIP under the condition that the maximum degree is bounded by a constant.