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Three, four, five, six, or the complexity of scheduling with communication delays. (English) Zbl 0816.90083
Summary: A set of unit-time tasks has to be processed on identical parallel processors subject to precedence constraints and unit-time communication delays; does there exist a schedule of length at most $$d$$? The problem has two variants, depending on whether the number of processors is restrictively small or not. For the first variant the question can be answered in polynomial time for $$d= 3$$ and is NP-complete for $$d= 4$$. The second variant is solvable in polynomial time for $$d= 5$$ and NP-complete for $$d= 6$$. As a consequence, neither of the corresponding optimization problems has a polynomial approximation scheme, unless $$P= \text{NP}$$.

##### MSC:
 90B35 Deterministic scheduling theory in operations research 65Y05 Parallel numerical computation 90C60 Abstract computational complexity for mathematical programming problems
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##### References:
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