Scheduling balanced task-graphs to LogP-machines

This article discusses algorithms for scheduling task graphs G V E to LogP machines These algorithms depend on the granularity of G i e on the ratio of computation v and communication times in the LogP cost model and on the structure of G We de ne a class of coarse grained task graphs that can be scheduled with a performance guarantee of Topt G where Topt G is the time required for the optimal makespan Furthermore we de ne a class of ne grained task graphs that can be scheduled with a performance guarantee approaching Topt G for increasing problem sizes The discussed classes of task graphs cover algorithms such as Fast Fourier Transformation Stencil Computations to solve partial di erential equations matrix multiplication etc