The complexity of scheduling problems with communication delays for trees

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Scheduling problems with interprocessor communication delays have been shown to be NP-complete ([PY88],[C90],[CP91],[P91]). This paper considers the scheduling problem with the restriction that the underlying DAGs are trees and each task has unit execution time. It is shown that the problem remains NP-complete for binary trees and uniform communication delays. The same holds for complete binary trees, but varying communication delays. On the other hand, by a nontrivial analysis a polynomial time algorithm is obtained that solves the problem for complete k-ary trees and uniform communication delays.