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Conceptual and algorithmic tools are developed as a foundation for a theory of scheduling complex computation-dags for Internet-based computing. The goal of the schedules produced is to render tasks eligible for allocation to remote clients (hence, for execution) at the maximum possible rate. This allows one to utilize remote clients well, as well as to lessen the likelihood of the "gridlock” that ensues when a computation stalls for lack of eligible tasks. Earlier work has introduced a formalism for studying this optimization problem and has identified optimal schedules for several significant families of structurally uniform dags. The current paper extends this work via a methodology for devising optimal schedules for a much broader class of complex dags, which are obtained via composition from a prespecified collection of simple building-block dags. The paper provides a suite of algorithms that decompose a given dag {\cal G} to expose its building blocks and an execution-priority relation \triangleright on building blocks. When the building blocks are appropriately interrelated under \triangleright, the algorithms specify an optimal schedule for {\cal G}.
Internet-based computing, grid computing, global computing, Web computing, scheduling dags, dag decomposition, theory.

M. Yurkewych, A. L. Rosenberg and G. Malewicz, "Toward a Theory for Scheduling Dags in Internet-Based Computing," in IEEE Transactions on Computers, vol. 55, no. , pp. 757-768, 2006.
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