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The critical path of a group of tasks is an important measure that iscommonly used to guide task allocation and scheduling on parallel computers.The critical path is the longest chain of dependencies in an acyclic taskdependence graph. A problem arises on heterogeneous parallel machines wherecomputation and communication costs can vary between different types ofprocessor. Existing solutions for heterogeneous machines attempt to estimatethe critical path using average values of computation and communication costs.However, this ignores opportunities to match specific tasks to specific classesof processor and communication links, and can result in quite misleading pathsbeing identified as critical. We argue that an accurate critical path mustconsider the mapping of tasks to classes of processor and communication links.We formulate a polynomial time algorithm to find such a critical path. OurCritical Earliest Finish Time (CEFT) algorithm finds both the length of thecritical path and an allocation of tasks to processors on that path. Wecompared CEFT experimentally to existing approaches such as averaging executiontimes across processors. The latter approach fails to accurately model theexecution cost of tasks, and as a result fails to identify a correct criticalpath in 83.99% of cases in our experiments. We also adapted a criticalpath-oriented scheduling algorithm (CPOP) to use our critical path algorithmand found that the resulting schedules are faster.

Mutual Inclusivity of the Critical Path and its Partial Schedule on Heterogeneous Systems