Introduction to Algorithms
GridAnt: A Client-Controllable Grid Work.ow System
HICSS '04 Proceedings of the Proceedings of the 37th Annual Hawaii International Conference on System Sciences (HICSS'04) - Track 7 - Volume 7
The Grid 2: Blueprint for a New Computing Infrastructure
The Grid 2: Blueprint for a New Computing Infrastructure
Workflow applications in GridLab and PROGRESS projects: Research Articles
Concurrency and Computation: Practice & Experience - Workflow in Grid Systems
Formal Analysis of Workflows Using UML 2.0 Activities and Graph Transformation Systems
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Allocating Series of Workflows on Computing Grids
ICPADS '08 Proceedings of the 2008 14th IEEE International Conference on Parallel and Distributed Systems
Deadline division-based heuristic for cost optimization in workflow scheduling
Information Sciences: an International Journal
Theoretical Framework for Eliminating Redundancy in Workflows
SCC '09 Proceedings of the 2009 IEEE International Conference on Services Computing
Towards critical region reliability support for Grid workflows
Journal of Parallel and Distributed Computing
DAGMap: efficient and dependable scheduling of DAG workflow job in Grid
The Journal of Supercomputing
PGWFT: a petri net based grid workflow verification and optimization toolkit
GPC'08 Proceedings of the 3rd international conference on Advances in grid and pervasive computing
A grid workflow language using high-level petri nets
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
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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.