Computing workflows in heterogeneous multiprocessor systems are frequently modeled as directed acyclic graphs of tasks and data blocks, which represent computational modules and their dependencies in the form of data produced by a task and used by others. However, for some workflows, such as the task schedule in a digital signal processor may run out of memory by exposing too much parallelism. This paper focuses on the data allocation and task scheduling problem under memory constraints, and concentrates on shared memory platforms. We first propose an integer linear programming model to formulate the problem. Then we consider the problem as an extended flexible job shop scheduling problem, while trying to minimize the critical path of the graph. To solve this problem, we propose a tabu search algorithm (TS) which combines several distinguished features such as a greedy initial solution construction method and a mixed neighborhood evaluation strategy based on exact evaluation and approximate evaluation methods. Experimental results on randomly generated instances show that the the proposed TS algorithm can obtain relatively high-quality solutions in a reasonable computational time. In specific, the tabu search method averagely improves the makespan by 5-25\% compared to the classical load balancing algorithm that are widely used in the literature. Besides, some key features of TS are also analyzed to identify its success factors.