Scheduling with Interjob Communication on Parallel Processors
Consider a scheduling problem in which a set of jobs with interjob communication, canonically represented by a weighted tree, needs to be scheduled on m parallel processors interconnected by a shared communication channel. In each time step, we may allow any processed job to use a certain capacity of the channel in order to satisfy (parts of) its communication demands to adjacent jobs processed in parallel. The goal is to find a schedule with minimum length in which communication demands of all jobs are satisfied.
We show that this problem is NP-hard in the strong sense even if the number of processors and the maximum degree of the underlying tree is constant. Consequently, we design and analyze simple approximation algorithms with asymptotic approximation ratio Open image in new window in case of paths and a ratio of Open image in new window in case of arbitrary trees.
KeywordsSchedule Problem Capacity Constraint Dependency Graph Approximation Factor Parallel Processor
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