Consider the execution of a parallel application that dynamically generates parallel jobs with specified resource requirements during its execution. We assume that there is not sufficient nowledge about the running times and the number of jobs generated in order to precompute a schedule for such applications. Rather, the scheduling decisions have to be made on-line during runtime based on incomplete information. We present several on-line scheduling algorithms for various interconnection topologies that use some a priori information about the job running times or guarantee a good competitive ratio that depends on the runtime ratio of all generated jobs. All algorithms presented in this paper have optimal competitive ratio up to small additive constants.