This letter deals with the problem of assigning tasks to the processors of a distributed computing system such that the sum of execution and communication costs is minimized. If the number of processors is two, this problem can be solved efficiently using the network flow approach pioneered by Stone. This problem is, however, known to be NP-complete in the general case, and thus intractable for systems with a large number of processors. Recently, an optimal algorithm with the time complexity of O(n2m3 log n) has been suggested for the problem of assigning m interacting tasks to a linear array of n processors. They solved the problem by using the two-terminal network flow approach. In this letter, we propose a multiterminal network flow approach for the task assignment problem in homogeneous linear array networks. The task assignment problem for a homogeneous linear array network of n processors is first transformed into (n-1) two-terminal network flow problems, and then solved in time no worse than O(nm3) by applying the Goldberg-Tarjan's network flow algorithm for each two-terminal network flow problem.