**Max-min algorithm**

8 Will-be-set-by-IN-TECH

equal load distribution based on the computing resources capacity. Our work is different

• While we deal with workflow, the work in Mello et al. (2007) considers a group of single

• In our work, The resources are reserved, whereas Mello et al. (2007) does not consider the

Related to the mapping task graph to resources, there is also the multiprocessor scheduling precedence-constrained task graph problem Gary et al. (1979); Kohler et al. (1974). As this is a well-known problem, the literature has recorded a lot of methods for this issue, which can be classified into several groups Kwok et al. (1999). The classic approach is based on the so-called list scheduling technique Adam et al. (1974); Coffman et al. (1976). More recent approaches are the UNC (Unbounded Number of Clusters) Scheduling Gerasoulis et al. (1992); Sarkar (1989), the BNP (Bound Number of Processors) Scheduling Adam et al. (1974); Kruatrachue et al. (1987); Sih et al. (1993), the TDB (Task Duplication Based) Scheduling Colin et al. (1991); Kruatrachue et al. (1988), the APN (Arbitrary Processor Network) Scheduling Rewini et al. (1990), and the genetic Hou et al. (1994); Shahid et al. (1994). Our problem differs from the multiprocessor scheduling precedence-constrained task graph problem in many factors. In the multiprocessor scheduling problem, all processors are similar, but in our problem, RMSs are heterogeneous. Each task in our problem can be a parallel program, while each task in the other problem is a strictly sequential program. Each node in the other problem can process one task at a time while each RMS in our problem can process several sub-jobs at a time. For these reasons, we cannot apply the proposed techniques to our problem because of the

In recent works Berman et al. (2005); Blythe et al. (2005); Casanova et al. (2000); Ma et al. (2005), authors have described algorithms which concentrate on scheduling the workflow with parameter sweep tasks on Grid resources. The common destination of those algorithms is optimizing the makespan, defined as the time from when execution starts until the last job in the workflow is completed. Subtasks in this kind of workflow can be group in layers and there is no dependency among subtasks in the same layer. All proposed algorithms assume each task as a sequential program and each resource as a compute node. By using several heuristics, all those algorithms perform the mapping very quickly. Our workflow with the DAG form can also be transformed to the workflow with parameter sweep tasks type, and

Min-min uses the Minimum MCT (Minimum Completion Time) as a measurement, meaning that the task that can be completed the earliest is given priority. The motivation behind Min-min is that assigning tasks to hosts that will execute them the fastest will lead to an overall reduced finished time Berman et al. (2005); Casanova et al. (2000). To adapt the min-min algorithm to our problem, we analyze the workflow into a set of sub-jobs in sequential layers. Sub-jobs in the same layer do not depend on each other. With each sub-job in the sequential layer, we find the RMS which can finish sub-job the earliest. The sub-job in the layer which has the earliest finish time, then, will be assigned to the determined RMS. A more detailed

from the work of Mello et. al. in two main aspects.

jobs but with no dependency among them.

thus we have applied all those algorithms to our problem.

description about the algorithm can be seen in Quan (2007).

resource reservation context.

characteristic differences.

**Min-min algorithm**

Max-min's metric is the Maximum MCT. The expectation is to overlap long-running tasks with short-running ones Berman et al. (2005); Casanova et al. (2000). To adapt the max-min algorithm to our problem, we analyze the workflow into a set of sub-jobs in sequential layers. Sub-jobs in the same layer do not depend on each other. With each sub-job in the sequential layer, we find the RMS which can finish sub-job the earliest. The sub-job in the layer which has the latest finish time, will be assigned to the determined RMS. A more detailed description about the algorithm can be seen in Quan (2007).
