Dynamic Parallel Schedules (DPS) is a high-level framework for developing parallel applications on distributed memory computers such as clusters of PCs. DPS applications are defined by using directed acyclic flow graphs composed of user-defined operations. These operations derive from basic concepts provided by the framework: split, merge, leaf and stream operations. Whereas a simple parallel application can be expressed with a split-leaf-merge sequence of operations, flow graphs of arbitrary complexity can be created. DPS provides run-time support for dynamically mapping flow graph operations onto the nodes of a cluster. The flow graph based application description used in DPS allows the framework to offer many additional features, most of these transparently to the application developer. In order to maximize performance, DPS applications benefit from automatic overlapping of computations and communications and from implicit pipelining. The framework provides simple primitives for flow control and load balancing. Applications can integrate flow graph parts provided by other applications as parallel components. Since the mapping of DPS applications to processing nodes can be dynamically changed at runtime, DPS provides a basis for developing malleable applications. The DPS framework provides a complete fault tolerance mechanism based on the dynamic mapping capabilities, ensuring continued execution of parallel applications even in the presence of multiple node failures. DPS is provided as an open-source, cross-platform C++ library allowing DPS applications and services to run on heterogeneous clusters.