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This paper addresses task assignment problem fortree-structure task model on heterogeneous multicore embedded systems with time constraint considering both execution time and communication load. The goal is to minimize the total system cost for a given task graph representing a set of tasks and data dependencies in a heterogeneous multicore systemwhile the time constraint is satisfied. Instead of assigning all the tasks to processors of the same type in a homogeneous environment, heterogeneous task assignment usually can reduce the system cost by exploring various capacities and costs in a heterogeneous multicore system. The general heterogeneous assignment problem is NP-complete. In this paper, we show that optimal task assignment can be found for some widely-used, special task graphs, such as tree-structure graph, using dynamic programming. A dynamic programming algorithm, the Tree Assign (TA) algorithm, is proposed in this paper to solve the heterogeneous task assignment problem for tree-structure task graphs. The experimental results show that our algorithm reduces the total system cost by 31.8% compared with assignment results on homogeneous multicore systems. Also, our algorithm achieves an average cost reduction by 21.9% compared with greedy algorithm.