Dynamic task assignment in heterogeneous linear array networks for metacomputing

In a heterogeneous computing system, the tasks of a program must be assigned to the heterogeneous machines so as to utilize the computational capabilities and resources of the system efficiently. This paper deals with a dynamic task assignment problem in heterogeneous computing systems, which permits each task to be relocated from machine to machine during the execution of a program. This problem is known to be NP-complete in the general case. In this paper, we extend the network-flow approach of C.-H. Lee, D. Lee and M. Kim (1992) to dynamic assignment for metacomputing. The dynamic assignment problem for a linear array network is first transformed into the network flow problem, and then solved by applying the Goldberg-Tarjan´s (1988) network flow algorithm in time not worse than O(n²m²φ² log nmφ), where n, m, and φ are the numbers of machines, tasks, and phases of program execution, respectively