In deadline-constrained wireless sensor net-works (WSNs), the quality of aggregation (QoA) is determined by the number of participating nodes in the data aggregation process. The previous studies have attempted to propose optimal scheduling algorithms to obtain the maximum QoA assuming a fixed underlying aggregation tree. However, there exists no prior work to address the issue of constructing optimal aggregation tree in deadline-constraints WSNs. The structure of underlying aggregation tree is important since our analysis demonstrates that the ratio between the maximum achievable QoAs of different trees could be as large as O(2D) , where D is the deadline. This paper casts a combinatorial optimization problem to address the optimal tree construction for deadline-constrained data aggregation in WSNs. While the problem is proved to be NP-hard, we employ the Markov approximation framework and devise two distributed algorithms with different computation overheads to find close-to-optimal solution with bounded approximation gap. To further improve the convergence of the Markov-based algorithms, we devise another initial tree construction algorithm with low-computational complexity. Our experimental results from a set of randomly-generated scenarios demonstrate that the proposed algorithms achieve near optimal performance and appreciably outperform methods that work on a fixed aggregation tree by obtaining better quality of aggregation