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On the complexity of scheduling with large communication delays. (English) Zbl 0947.90573
Summary: Given a directed acyclic graph (dag) with unit execution time tasks and constant communication delays \(c\geq 2\), we are interested in deciding if there is a schedule for the dag of length at most \(L\). We prove that the problem is polynomial when \(L\) is equal to \((c+1)\), or \((c+2)\) for the special case of \(c=2\), and that it is NP-complete for \((c+3)\) for any value of \(c\), even in the case of a bipartite dag of depth one.

90B35 Deterministic scheduling theory in operations research
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