LDAG: A New Model for Grid Workflow Applications

Grid workflow and its application are one of main focuses of Grid Computing. Due to data or control dependencies between tasks and the requirement of no directed circuit, Directed Acyclic Graph (DAG) is a natural model for Grid workflow, and has been extensively used in Grid workflow modeling. For some workflow applications, there may exist another requirement that each task should be accomplished at an expected stage, that is, at a given level. In this paper, we discuss such workflow applications in depth, and propose a new DAG model, which we called LDAG. In LDAG, each node possesses a level. Several cases of the level of nodes are discussed in detail. For a reasonable one of these cases, we propose the topological sorting algorithm. The algorithm consists of two phases, namely Level Adjusting and Topological Sorting. We discuss some relevant problems, such as choice of stack or queue, the determination of directed circuit, complexity of the algorithm, etc. The experiment and analysis of LDAG and topological sorting algorithm show its correctness and efficiency in modeling grid workflow. Key-Words: Directed Acyclic Graph (DAG), LDAG; Grid workflow; Level; Topologic sorting; Directed circuit